Laplace Transformations | HRRL | HPCL

[00:00:00]Hi students. So kids, in the HRRL paper, a question also comes from Laplace transform. Ok?

[00:00:06]I did not make you do this.

[00:00:08]also comes from the Laplace transform.

[00:00:10]A question comes in your technical part. So what's in it for you? Like if there is any function, then you will ask what is the Laplace transform of any function? So whatever answer will provide you four options. Ok? So these are the answers and the functions. Will write l of f like this or will write what is the Laplace of this function? Ok? So here l is for Laplace. So you know the Laplace variable is s.

[00:00:41]And these functions are given here.

[00:00:44]As if he asked, what will be the value? Laplace transform of 1, right?

[00:00:51]So if there is one function then what will be its value? 1 / s similarly t is Laplace of t its value is 1 sq t to the power n is the value of nial over s power n + 1ial is the function e to the power at so its value is 1 s - a sin at a over s² + a² cos at s over s² + a² a is any constant.

[00:01:19]Ok? So what's there to remember about sin at and cos at? In both cases, s² + a² will appear in the denominator. Inside the numerator, a will come inside sin. s will come inside cos.

[00:01:31]Similarly, there is also the formula for sin at and cos 80.

[00:01:34]Just what is the difference between them? In that, sin will come negative in the denominator below. Look, if there was a plus inside sin at, then there is a minus sign in the formula inside sin at.

[00:01:44]in the denominator. Similarly, what is in cos at and cos at? Just the sign will change.

[00:01:50]So this way you can remember.

[00:01:52]After this, if t is added next, t of sin at here is h. Ok? These become two functions: sin at and t, and then cos at.

[00:02:03]So in that case it's going to be 2as over s² - a² squared and so cos is going to be s² + a² over that. Ok? So these are the two formulas. After this, these are the formulas. Look, t is also placed before sin. I did that by doing cos at and sin at. I also tried adding t in front.

[00:02:27]After this comes sin at and cos at, t is placed before them.

[00:02:33]If we put a t in front of this, then this is the square of 2s over s² + a² to the power of a². Ok?

[00:02:40]This is the formula for cos at. Similarly, if we put t² before t², then these are the formulas. That is, it is the Laplace transform. Ok? If these are functions then their Laplace transform is: Now the question that HRRL had asked was this question.

[00:02:53]This question came in the 2024 exam. He had given it like this. The square of s² - a² over s² + a² is the Laplace transform of this four, so he gave you that. Options were given and you had to choose the correct answer and you should know it. Look who is this matching value with? x² -a² to the power square of x² + a².

[00:03:21]So what did you give this to?

[00:03:27]This one in it. Ok? So your answer was to come directly t cos at okay? So there were four options and the option among them, na t cos at, was the correct answer. So he said this and wrote it like this, this is the Laplace transform of, so you picked t cos at or he will write it like this, Laplace of t cos at, so you can pick this answer also.

[00:03:53]So in this way he can ask you questions. So a question has come up from this, that is why I did not get it done for you.

[00:03:59]This question of yours comes under the technical part.

[00:04:01]So you should revise these ones also. Ok?

[00:04:04]Take a screenshot of it.

[00:04:07]Remember them in any way you like. This is important. Ok? Thank you.