Question

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

Answer 1

Answer:

$L(tsinn^2 t)=\dfrac{2sn^2}{s^2+n^4}$

Step-by-step 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

$L(t^nf(t))=(-1)^n\dfrac{d^nF(S)}{dS^n}$

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

So $F(s)=\dfrac{ n^2}{S^2+ n^4}$

Find the derivative of F(s)    

$\dfrac{dF(S)}{dS}=\dfrac{-2sn^2}{s^2+n^4}$

So

$L(tsinn^2 t)=\dfrac{2sn^2}{s^2+n^4}$