13 1 OSCILLATIONS INTRO S H M

Added: 2026-05-17

[00:00:00]13th lesson oscillations part one in motion based timeline we studied about the linear motion or translated motion and then in motion plane we studied about the motion of a body in two dimensions that is when a body projectile projected into a the velocity along x-axis and yaxis motion in two directions and then in the same motion we studed about the circular motion.

[00:00:34]Whenever body moves in a central path the body will act towards the center of the central path by a force called center force and here it will have two accelerations. One is towards the center acceleration one is this one tangential acceleration. So that is one type of motion in physics. If you take the motion of your body, this motion can be divided into three types. Number one, translator motion also called a linear motion. Your body is said to be in translated motion if it is moving in a straight line path. straight line or central circular motion or rotation motion actually both are not same but not same circular motion if a body moves in a circular part the axis is at the center so body moving around the axis rotating motion the axis is passing to the body moving about it aisle to the body circle motion. The axis is this is the path of the body and this is the axis c motion almost motions. The third one oscillator motion vibrational motion. So these are the three types of motions in physics. Why we have studied about these two motions in motion in motion loss of motion also we studied about motion work also we studied loss of motion and motion of the body and then in system of particles and motion we stud about the rotation motion in gravation also we stud motion as well as rotational motion You have to axis you have to roll around the sun. So both motions we studed there. So these two are completed in the seven.

[00:03:06]Now this lesson is about the third type of motion called motion. But before learning about these motion student friends, we should know the value or the meaning of periodic [Music] motion. Periodic motion. The motion of a body is said to be periodic.

[00:03:34]Motion of your body is said to [Music] be it repeats after repeating motion after equal intervals of time is called periodic motion. Anything that comes after is called. For example, if you take a pendant is a displacement there and coming there goes to the other side and comes back. This is what is this is it.

[00:04:29]Now after 0 seconds we can see the here.

[00:04:33]After 2 seconds we saw the pen reaching this point. After 4 seconds it is reaching to the same point. After 6 seconds it is reaching this point. So after time it is repeating this motion.

[00:04:48]Then it is called periodic motion. Periodic motion. Today January 1st 2025 after 365 days the same day will come in the calendar after 12 months of period we will the same situation same celebrations today also come at the same time 230 so I repeat I am repeating coming after. So my motion is also motion. If you take a spring here and the block is connected to the spring of mass, this is the base. Now this is the unstructural spring. What is this?

[00:05:47]Unstretch. So lateral length of the spring is this much. Now if I move this here will be touching and release it comes back to this position. So whether the motion is or not it is coming up to here going back after let us say 10 seconds then from here then after 10 seconds the same 10 seconds which is this one is it periodic or not? So this is also clear. This is clear. How is this clear?

[00:06:26]Because this motion is motion of the body is repeating after motion.

[00:06:41]Similarly, it will come to the same position. So this motion is also periodic motion rotational here connected to is periodic and one more example motion half. So these are the some of the examples for periodic motion. Periodic motion. But the next one is motion. What is the difference between periodic motion and oscillating motion? Oscillative motion students. This is a body. This must be motion must be and two and four. What is this? Two and four pixel point. Two and four motion. In this examples, what are oscillating motions? First one we will see. First one periodic motion. This motion motion of a B of a pendulum super pendulum. Now if you displace the ball to one position it is going there coming back going there coming back going there coming back is it two and four point or not above this middle point it is going two and four two and four. So this is peri as well as oscillator motion. Come to this question to your sple is it not because it is coming to the same point of equal inverse of time and then motion of the sun. Is it periodic or not? After 364 days it is reaching the same position. Same point same point same point same point. So this is also periodic but this is not two and four.

[00:09:24]This is not oscilly. This is not oscillator here. So what is oscilly motion? It is a periodic motion plus two under flow motion. Pi plus two motion is called motion. Example same example you can give the same example.

[00:09:46]Example of oscillator motion is number one oscillations of of pendum oscillations of pendum is oscillating motion. Example number two, oscillations made by by a block. Oscillations made by a block connected to a spring. Connected to a string. Example of oscillating motion.

[00:10:31]Number three, oscillations of Okay. Branch off tree branch off tree branch purpose of it two and four motion whether the motion is repeated or not repeating. So going up and coming down going up and coming down. So it is periodic and then two and four. So that is also possible. So we can give so many examples for this oscillator motion. If you take this fan the motion of the blade of the is it is coming to the same position after maybe 1 second or 2 second or 3 second or 0.3 second what sometimes is coming to the same position. But is it no it is not moving two and four is not moving like this. This is not two and four. It is rotating about the axis here. Now suppose if you insect insect insect and when I say my hand is climbing a smooth steel plate smooth steel plate is very small smooth and reaching some height it is falling down once it is trying to reach and falling down. The same thing can be seen in case of frog also. Front will climb trying to climb there. It will then fall down. Once you have to reach and fall down. Now if you take this inside and if you want to find out if you want to draw the height of nature of this one and then height come back in very starting the journey from this position climbing the steing this much height it is falling down once again climbing but falling down is like more to understand to climb It is taking more time but to fall down it is taking less time. So let us say this is the time taken to reach this to climb to climb. So this is taking this much time then it is falling down immediately. It is taking less time. What's the meaning of this one? It is taking more time to time. It is taking less time to solve. Once again it is taking Same time falling down. Same time falling down. Same time falling down. So if you take this one and this one as a hole, it is starting here going up going up and falling down going up and falling down going up and falling down. Means the motion is repeated at the same level of 15. So what is the time period here? Once again the reach the bottom t seconds the motion will be repeated.

[00:13:59]So it clear motion. Is it clear? Can I say it is oscillating? Is it oscillating or not?

[00:14:11]Going up or coming on? Yes.

[00:14:15]Similarly, a freely falling body falling body without a friction without friction. Free falling body which is equal to U + half GT². What is the initial velocity of body? Zero. So how much resourcing the ground is falling body colliding the ground elastically elastically. If the body strikes it to you it rises with U only mean it reaches the same height once again it falls rises falls rises false rises false rises. Is it true for motion? Is it clear or not?

[00:15:10]periodic oscillating motion. So here as h is direct to t² we are getting if two physical quantities are direct to each other which we get a bot to b what we get linear motion linear relation stere Yeah, rectangle to B square. You take A here, B here.

[00:16:10]You keep a b= k= k² some conant if a z you keep b 0 everything is now b1 what you get keep b1 1 k a k b2 4 this is 4k b - 2 - Is it 4K? Is it 4K? So now I will draw this one. So what type of graph I'm going to get? If two physical quantities are each other such that power one is one power one is two. If it is the case then whatever you get. Now I'm getting B 1 2 3 and minus one. This is A. This is B. I'm taking 1 2 3 4 this side -1 - 2 like this. But if you can see even B is negative B is always positive. So this one is not equal for me. So only this one K 2 K 3K 4K. So what structure I'm going to get? A 0 B 0 B1 B1 A B2 A this side also same.

[00:17:56]This is called parabola. Is it clear?

[00:18:01]If two physical points are to each other passing through horizontal each other rectangular hyper rectangular hyperola Here is you get here h is it half g conant or not half conant gant hal t² so here b² so I'm taking b² b here I'm taking t² here so structure we get here what structure this also but here t cannot be negative right here b can be negative but here t cannot be negative so you don't make negative value here so you get the curve like this only once again like this like this like this like this when the time increases Is it now P increasing under this H also it will be within that range only within that range. So is it periodic or not? Is the motion is repeating after equals of time or not? Let us say this time is 10 seconds. This is 10. This is 10. This is 10. This is 10. This is 10.

[00:19:44]After every 10 seconds motion is repeating from here to here 20 seconds from here to here 20 seconds from here to here 20 seconds. So is it or not?

[00:20:01]Yes body striking going up striking going up. Is it two and four? Two and four. motion it is going to and from use two terms interchangeable that means first one oscillations second one vibrations actually speaking students these are two different words in physics but we can use Oscillations in terms of vibrations.

[00:20:41]Vibrations in terms of oscillations.

[00:20:44]What are oscillations?

[00:20:47]Two and four motion at a faster rate.

[00:20:58]Posture rate is mean to motion oscillations. And what are vibrations? Two and four motion relatively slow. Relatively slow means when compared to this this is slow. So these are called vibrations.

[00:21:30]Why I made a mistake? Oscillations are to slow students and this is a little faster rate. Vibrations of atoms. Vibrations of atoms. It is very fast. very fast for the answer of three branch. You should not you should not say vibrations of branch of tree because for two or 3 seconds it vibrates once it will branch of but season ar 910 34 739 9 once again once again you motions at based on the number of vibrations made by cium atom we are defining 1 second 1 second. So this is very large frequency of tuning for you know tuning for frequency what we can say vibrations or oscillations vibrations of flow we should not use oscillations but in a question paper or in a ne exam or in a J exam they may give oscillations of a tuning for this is not wrong Thus even though these two are two different words but we can use oscillation in terms of vibrations or vibrations and there is no change no change according to physics while fraing the question while solving the problem you can use either the oscillations or vibrations interchangeably no problem but actually you should know vibrations are too Fast and also so this is it.

[00:23:51]Now our lesson is about oscillations. So first we will study about oscillating motion in detail.

[00:24:02]So in the motion I will take one spring connected to a block spring connected to a block and this is the natural length of spring. What is this? What is this natural length of spring? So without extension what is the natural spring is this much and this is the block. Now if you displace this block by distance X what happens? If you displace this block to this position what happens?

[00:24:50]spring will extend and restoring force will be developed in the spring. Which force restoring force develop in the spring? So how to find which direction when the block is moving towards right spring towards right now left direction. So who is bringing this ball from here to here? Spring force. The restor the spring. So what is the restoring force?

[00:25:32]This force is called spring force. We have known this as s and we studed this in the previous lessons which is to elongation compression compression students. When the displacement is towards right, spring force will be towards left. When the spring towards right, spring force towards left. When the spring is compressing towards towards right, spring will push the block towards right. So fs and extension or elongation or compression will be opposite to each other. Is it clear? I move the ball from here to here. Spring is following this block back following this block back.

[00:26:32]Similarly, if I compress the spring by pushing the block towards this side, spring will push it back. So, spring will try to push the block towards to position position. Just like if you take a ball and if you keep a spear here, if you dispose it from here to here, it has move. Now this will try to come back and try to go up come back because this mg acting downwards and this component is mg sin theta. How much mg sin theta is the restoring force in this case component acting? We are not pulling it down yet is pulling this down. That component is called sin theta. It is pulling this down. After reaching here because it gains an acceleration because of the force it gets an acceleration and it will try to go up.

[00:27:34]Now somebody's pulling back. Please not somebody reach here. Is it two motion? So this is motion. What is two? First one.

[00:28:00]7 2 and 4. Now here in this example this example every time it is displace by distance X direction here very simple FS - X F is equal to minus K into X what is K force conant R spring conant this is a spring conant This is for minus I'm going to use the same expression here spring force f is equal minus kx. What is the meaning of this one? If the displacement of compulsion is one direction, spring force will act in the upward direction to bring the block or the ball or the spear to it position.

[00:29:12]That's why this spring force is also called restoring force. Why restoring? It is a restoring it position. Suppose if you take big one. So here by holding these ropes if somebody pushes you you will go this side and comes back here and you put this wheel position. Is it oscillating motion or vibrations? Why oscillating? Slow motion.

[00:29:59]This So this is oscillations of of a swing. So these areations. So in this also when the person moves to this position his weight is acting downwards who is moving his back side is theta the max theta it will come back due to this restoring force.

[00:30:35]So here what is restoring force here can I say minus mg sin theta minus mg sin theta. But here we have one more motion which is actually motion called simple harmonic motion also called yes H simply. So this entire yes H simple harmonic motion.

[00:31:14]So what is this harmonic motion in harmonium harmonium? So that is also periodic.

[00:31:37]After equivalence of time the same sound will repeat in the harmonium. That is harmonic motion. The periodic motion is also called harmonic motion. So what is harmonic? This is motion motion motion. Now in this periodic motion any motion for any periodic motion we can use this formula for any periodic motion we can write = -x all power for any harmonica periodic muscle we can say the restoring force is equal to k into x yeah students n is equal to 1a 3a 5 and 7 and so on all all odd numbers only all odd numbers so why this is odd numbers we'll see now the same thing I'm getting is moving in this part in this part in this part I'm writing f= mg sin theta which is = minus kx where x is this displacement from the mutation from the main position. X is the displacement. Always we have to measure this X main position. So in this formula what is your students? What the name of this one?

[00:33:16]Retoring force. What is this? Displacement of the body.

[00:33:27]displacement from main position and it should be always measured from here always position. So if the body comes from here to here, what is displacement? This is you have to measure from here only. If comes from here to here, what is displacement? Don't measure from here to here. Displacement of the comes here is not this much from here to here. Always measure from here to here. Understood? X must be measured from always displacement from main position only. That is the condition in this harmonic motion that is equal to minus kx power. Yeah. Now in this problem if the person moves towards right towards right by distance. Yes. Is it positive or negative? This is yaxis. This is xaxis.

[00:34:25]Is it positive or negative? Positive. So what is the force here? I write from A to B. So I move from A to B. So from A to B what is X positive? Because I have to measure the distance only from distance only from main position and I measuring this alone positive X ais that's why X is positive. Then what is the restoring force formula?

[00:34:59]restoring force - k x^ I will take = 1 now = 1 so x is positive positive for one positive positive to so force is negative that means jo from here to here how acting along negative x-axis body move towards right side body move towards right side. Body means the person is more towards right side but force is acting towards left side. Then from B to A I B from A to C to C from A to C.

[00:35:52]Then C X pos2 X positive X is negative because I measuring from mean to left side so I'm taking this as Yaxis from this side this is negative X is X is then what is the restoring force - K - X power 1 So minus of minus.

[00:36:21]So how the restor is acting? If you move from here to here, some force is acting towards positive xaxis. It is trying to bring it back. Is it clear? So whether displacement is on right side force on left side, displacement is on right side. Left side will be right side. So this is this can represented by this formula. What is the formula? F = - X must be N must be R number any odd number positive R number. What happens if we take two here? You just check it. What is = 2 k x² pos 2² pos2 no problem here - x² it's - x² + x² + force is acting on xaxis that if this is the two students = 2. What is this value?

[00:37:38]- 2 + here also minus here also minus. No, that's why it should be always number three. You enter here + x is plus - x - x - - plus. That's why what is the condition for harmonic motion = - x is 1 3 5 7 so on if it is even number that is not that cannot get force you force only one direction to get force in opposite direction should be odd value should be odd number suppose in this if= 1 here I'm waiting = - k in this n = 1 that is the simplest harmonic motion right 1 is the simple one simple one 3 n 5 n= 7 so complicated harmonic motion when the harmonic motion become simple then analy that's simple That's what we call as simple harmonic motion. One more motion to be simple motion is a simple simple should be it may be 1 3 4 5 7 and so on any other number these are emotions because yes motion I'm going to use the term yes h what is that simple harmonic motion for living body is executing simple harmonic motion there are three conditions if your body for these three conditions then only body is said to be in simple harmonic motion. So what are those three conditions? First we discuss the first one motion should be periodic motion should be periodic motion. Second one motion should be two and four position.

[00:40:50]Fix position.

[00:40:56]Obseration of the particle.

[00:41:16]Absolut towards the main position. Always back towards the main position.

[00:41:28]And the ear is directly proportional to displacement.

[00:41:46]displacement and opposite to it and opposite direction to displacement.

[00:42:02]These are the three conditions for a part in the summary [Music] conditions for what the first condition motion should be periodic. Motion should be periodic. If you take the motion of planet or sun is it periodic or not periodic. So okay then motion should be two and four. Is it motion? So motion motion around the nucleus are not simple harmonic motions. They are just motions. They are just real motions. So first condition is second condition position. Third one most important one. Whenever your body is dispersed from it position, always the exelation of the body should always try to bring it back to the main position. Just about curl, swing, spring, simple, anything. Suppose if you take a simple and if I take it here, this is called main position. Main position. So here from position if you disable position or not the position position see always towards main position.

[00:43:50]Yes. The acceleration acting means acting towards main position also acting towards main position acceleration. So force is acting towards main position. So observation of the part you should always assment means if you displace it to create distance to displacement. What's the meaning of this one? If you displace it for 10 m force will be the force equation simple harmonic motion = minus kx what will be the simplest harmonic motion the power must be equal to 1. Now in this case in this case when the particle is at the m position what is x? When the part reaches the position, what is X? Zero. Why? Just I told you this should be measured from mean position. To reach the new position, what is displacement? Zero. Then what was the force? What is the force? At the mean position minus K into 0. So get the mean position. Get the mean position. Force is zero. Can I say M0?

[00:45:24]4. Can I say a 0? Yeah. Clear. When x= 0 when x= suppose if you take the baba pendum I displace it this much. It moves like this. This is two one for motion about the main position about the main position. But if I take this after disputes this is these are theations made by the ball. What the difference here? When the displacement is small change in velocity what is the change in velocity rate of change of velocity is small is moving slowly. The displacement is more acceleration is more then it has to come back to it position at a greater speed but greater change in velocity change in the same time delta v by delta t is small is it clear? So X is small acceleration is small. When X is small, acceleration is small. When it is taken to this side, it is coming back slowly.

[00:46:33]When X is small, A is small.

[00:46:37]If it comes with a greater acceleration velocity. So acceleration displacement and one is there and is opposed to the left side right side. So force is acceleration. Is it clear? Now read the last sentence clearly. The acceleration of the part always the main position.

[00:47:10]Okay. It will come back to motion. If it is simple motion if it is it will come back. So every time it is coming back that's why we can say force towards position. Second one if displacement is small change in velocity is small is small. If displacement is small acceleration is more there are three points here. One is direction of acceleration. Second one with the displacement with the displacement direction. This is always position. If you take this side this side this side always position opposite to the opposite to the displacement and no displacement. That mean if the B is left alone for 3 hours nor dis so it won't be this one it won't have to give some small displacement and then it will startating the position. So oscillation should be start and the system will continue to oscillate continue to oscillate one [Music] more. Can you say all periodic motions are all periodic motions are the sun the nucleus is periodic or not? But is it?

[00:49:09]No. So some of the oscillating motion is periods. So what is these type of questions are very useful in assertion and reasons they like this all motions are not this is perception the reason they give what the They will give two statements. Statement one, statement two. All periodic motions are not. Do you give this one or not?

[00:50:01]For example, you reverse around the same motion but not motion.

[00:50:24]But now it is not possible. This is final. One more statement all example. This is motion. Is it periodic or not?

[00:50:51]Yes. oscillating is it periodic or not spring compressor and release it is oscillating is it for motion or not is it or not? So what we can say?

[00:51:19]Oh my no energy lost. No energy lost.

[00:51:44]For example students just one sentence here all periodic periodic they should repeat that motion after equal inverse of time after equal intervals of time. I just here it is moving this side going that side going this side. Is it oscillating or not? Is itating or not to and clear?

[00:52:10]But uh whether it is losing some energy or not. Why it is losing energy? Because of friction. Because of viscous force.

[00:52:19]What happens? Slowly. You can see my hand. What is happening here? Previously is moving from here to here because it has large energy. So large it can take more distance slowly. What is happening? What is happening? From here position the displacement is gradually decreasing. X decreasing. Can I say a decreasing? X decreasing. A decreasing.

[00:52:48]A decreasing means previously a was now a is finally it comes to rest. Can I say now has motion? Motion stop because of energy loss. If energy is not lost then the statement is 100% correct. What is that?

[00:53:14]All motions are periodic. If energy is not lost then they will continue. They are called undampations. These are called undampations. If you take the whole pendulums all blocks with pendulum but the pendulum is inside a vacuum chamber.

[00:53:35]Why vacuum chamber? If air is present in that one, air will always and finally some days after some days because of the viscosity of air it comes to rest.

[00:53:51]For that reason what they do generally they remove the so that it will continue to oscillate lifelong clear with the help of a uniform circular motion of the body comparing with uniform circular motion.

[00:54:20]S H N of a particle in contrast with uniform circular motion.

[00:54:42]Here there is a circle of Which part is moving? This is central path in which a part is moving.

[00:55:16]So in this I'm going to take the particle initially at this position. Particle at this position I will take this position as a remember students it is making under uniform central motion we generally denote this as UC. What is uniform central motion?

[00:55:42]There is no change in velocity or speed.

[00:55:46]Speed is not changing here. Speed is let us say 10 m/s. Here 10. Here 10. Here 10. Here 10. Here 10.

[00:55:56]So speed of the remains constant. What is speed remains constant. Now for this particle I kept one cloth here. I kept a cloth here or a screen. I call it a screen. What is this screen? And I kept a big light here. some light and then positive light onto this. This is a circular path. Imagine circular path. And if you see only this particle only the particle plus the shadow of the particle is formed on the screen from shadow will be formed on the screen. So this is the point where the shadow will be formed will be formed. So I call this as a position here. What is this position?

[00:57:10]Yeah. So from this position here I call this position as a after some time this particle this particle under motion in anticlockwise direction clockwise direction with angle velocity it is an angle angle velocity angle velocity constant velocity and constant speed both are constant that's why it is called uniform circle motion so this is the first position sometime B so the shadow of the screen this is B part see what is the position of this part on the screen after some time reaches B. What the position of this one B don't think that when the particle goes from A to B, B to C, C to D, color changes. No, I'm just using colors to to know the exact position clearly. That's it. Color of the body will not change the universal motion. So here particle moving like this position of the shadow is also changing. So the particle moves from A to B. Particle moving up. A B C D. The shadow of the particle is moving from A B C D. Is this in a straight line? Here part moving in a circle path.

[00:58:58]But here shadow moving in a straight line path. Now is coming back to position the shadow center comes to position here. And the power comes to position G.

[00:59:22]Then half revolution is completed. Then it is moving in circle. Particle is moving in uniform circular motion. Now next one particle comes to this position H. Is this H? Is this H? Then comes to I. Is this the position of the S on the screen? And then this comes to this position J. This is really the particle moving in a circular path or the shadow moving in a straight line path. Straight line path. Then particle comes to position K. Can I write K here? Same position of the shadow. And then part comes to this position L. This will be the shadow L and finally comes to Y.

[01:00:32]This is what happens. If you observe this motion and that motion clearly particle is actually under circular motion but the shadow of the particle executing two and four motion are not from this position two or four and four two and four. So it is this is why we are taking 10 seconds to complete oscillation. Shadow will take 10 seconds to complete oneation.

[01:01:13]Shadow making 100 oscillations. Sorry 100 revolutions. This sh also completed 100 revolutions.

[01:01:25]So is there any relation between uniform circular motion and a circular motion? Yeah.

[01:01:34]See producer is it or not? Yes. Yeah. When we can say please check those three points.

[01:01:44]First one is it creating whether the motion is repeated or not. Number two, two and four. Number three, when our body goes up, always it is trying to come back. When it is going down, always trying to go up. So acceleration always acting towards mean position and we will see whether a is x or not from this equation. Is it clear now what we doing? I will take this position position when t=0 when t=0 the particle in uniform central motion is at point and reach a point say when the time is= t the time= t after some maybe.1 second or 8 second or 2.8 N participles sometime sometime. Now what is the name of this line? Can I say of the circular path in which the particle is executing uniform circular motion? Can I call this as sorry R. What is this point of the path is and what is this? Is this also this is rad? This is new vector.

[01:03:15]Position has changed. Position has changed.

[01:03:19]Now we will we are writing equation for the displacement of the simple harmonic motion. We are taking this reference circle but we are studying this motion not this motion. We stud this motion motion plane and loss of motion. We studied universal promotion theory itself as well as what promotion we are discussing this. Yes.

[01:03:52]Yeah. For universal motion we found disment we found velocity. We found observation displacement velocity and observation.

[01:04:06]What are the symbols for motion? Angular displacement, angular velocity, angle accelerations. Theta omega alpha angle displacement, angle velocity, angular.

[01:04:21]Similarly also I need displacement of central motion, velocity of central motion, acceleration of motion. So what is displacement? We know the point displace should be measured only from main position. In this what is mean position? A is the mean position.

[01:04:42]Whenever you are finding displacement for SH always measure it from main position. So now from A to C shall from A to can I say this is displacement. Can I say this is displacement? Is it along Xis or Yaxis? So I will take the displacement after simple harmonic motion. Any particle, any particle executing S HM is called S H is called S H O. What is the simple harmonic oscillator? What is this super harmonic oscillator? So from now on I will use that word only that this is such this is sh only but still it is executing simple motion. So I call it as simple harmonic oscillator. What is that?

[01:05:55]So now can I say this is the displacement of SH? See this one is this y= both are same or not? Both are same or not. See the diagram. This is the displacement of SH.

[01:06:12]Is this the displacement of SH? Same distance. Now this is can I say this is angle displacement theta?

[01:06:23]So we know trigonometry. I want this. I know this. I want the opposite side. I know hypotenus. Which one I have to use?

[01:06:32]S. So I'm writing from the triangle. I will take this part. What? From triangle P C. What is sin theta? Opposite side hypotenuse. Y by R cross the What is Y sin theta? This is what is this? What is this Y? What is this Y?

[01:07:03]Y. What is this Y? Displacement measure from main position. Now this is Y1. What is this?

[01:07:12]This is Y2. This is Y3. This is Y4. Y5.

[01:07:17]Y 6. Y 7. Y8.

[01:07:21]from main position and the new position that's can you find Y 6 but this is a positive Y this is a negative that's the only difference above the mean position this is positive below the mean position this one should be negative that's the only difference now what is the max is this R or What is maximum? When the water reaches from here to here, this is called maximum displacement.

[01:08:00]Okay.

[01:08:03]Maximum displacement of R. Yes. H maximum displacement of simple harmonic oscillator is called amplitude is called amplitude in this diagram the amplitude is equal to radius of the circle. This is the max beond. This is the natural disment. The magnitude disment is called amplitude under a. So this is equal to how much?

[01:08:45]How much? So how this will change now? Y = a sin theta. What is velocity? Displacement.

[01:09:01]What is velocity? Displacement by 10. What is angle elastic? What is angle elastic? Angle is number 10. So what of theta omega? So what is y? What is y? A sin omega t. What is this equation? This is the displacement of particle in hm. What is this displacement of? Yes. H no equation y= sign. So here I got displacement of particle in h y = A sin omega t a sin omega. If you observe this equation, this y is a sinosal function.

[01:10:22]y is a sinosidal function. What is this sinosidal function friends? Listen you know this is sign table given by so here I'm writing theta value and sin theta value if theta is 0 sin 0 if theta is 30° sine 0.5 by 2 sin 45 1 by <unk>2 sin 60 by 2 sin 1. This is in the first quadrant. In the second quadrant, if you add this one sin 120, how much value? All students take all 70. Okay. S is positive. What is soo3 by 2? Sin 135, 1 by <unk>2, sin 150, 1 by 2, sin 180. Do you know all these values? Do you know these values? Now if you draw the graph for this one students by taking this values here theta. Now this is 0° 30° or 45= 60 90 120 150 180. So which of you get the magus one because sin 180 is 0 but sin 270 is - 1. So max value is + value is sin 270°us. So all the values li sin theta cannot be greater than one sin theta cannot be less than minus one.

[01:12:31]All val. So now the graph will be within this region only. Now it is maximum here minimum gear the graph will be like this. Have you seen this graph? Is it there in this curve? What is this?

[01:12:55][Applause] Now what is this value? 270 - 1 2 360 + this is cinos. So y also changes like this only.

[01:13:12]Why initially in this in this for example this screen first initially y increasing y and then decreases and then negative and then zero is it same or not 0 maximum 0 - 0 maximum 0 - 0 maximum 0 So Is [Music] it or not? Is it or not? Because this is sin theta. Suppose I write this as y= sin theta theta 0. Tell me what is y theta 0 theta 30° what is y theta = 45° y = theta = 60° theta = 90 so what is this Here what is the angle of mark? When the part is here, what is the angle displacement? Zero. Then what is the position of zero? Then what is displacement of this? Zero. Because I have to measure zero. Now when the angle displacement is 30° 30 30 angles 30 then what is here by 2 half of the when theta is 30= here by 2 when theta is 45 how much it is here when theta is It was 90 199 19 y= a tus y sin theta and y is a cinos function it is similar to the sign that you studed in mathematics that's why y= a sin omega t is the equation for finding the disle SH displacement of SH for Y= A sin omega T