Question

Laplace transform of t sint is​

Answer 1

Concept Introduction:-

The integral transformation of a real-valued derivative into a more sophisticated function is known Laplase transform.

Given Information:-

We have been given that  $t sint$

To Find:-

We have to find that the value of $t sint$

Solution:-

According to the problem

The Laplace transform of

$=(-1)^{1} \frac{d}{d s}(L\{\sin (t)\})\\L\{\sin (t)\}: \frac{1}{s^{2}+1}\\\frac{d}{d s}\left(\frac{1}{s^{2}+1}\right)=-\frac{2 s}{\left(s^{2}+1\right)^{2}}\\=(-1)^{1}\left(-\frac{2 s}{\left(s^{2}+1\right)^{2}}\right)\\=\frac{2 s}{\left(s^{2}+1\right)^{2}}$.

Final Answer:-

Laplace transform of t sint is​ $\frac{2 s}{\left(s^{2}+1\right)^{2}}$.

#SPJ3