Question

1. Find the Laplace transform of the function f(t)=tsin n^2 t.

Answer 1

`L(tsinn^2 t)=(2sn^2)/(s^2+n^4)`

Explanation:

Given

`f(t)=tsin n^2 t`

Here n is constant because f(t) is a function of t so n will be treated as constant.

We know that

`L(t^nf(t))=(-1)^n(d^nF(S))/(dS^n)`

Here given that f(t)=sin n^2t

So
`F(s)=( n^2)/(S^2+ n^4)`

Find the derivative of F(s)

`(dF(S))/(dS)=(-2sn^2)/(s^2+n^4)`

So

`L(tsinn^2 t)=(2sn^2)/(s^2+n^4)`