Best solutions to - "Find Laplace Transform of each following (a) tn..."

Brittney Lord

Answered question

2021-10-20

Find Laplace Transform of each following
(a) $t^{n}$ , (b) $c o s ω t$

Answer & Explanation

Nichole Watt

Skilled2021-10-21Added 100 answers

For A
We have to find Laplace transform of $t^{n}$ , that is $L {t^{n}}$
Now from the Laplace Transform table
$L {t^{n}} = \frac{n!}{s^{n + 1}}$
It shows that:
$L {t^{n}} = \frac{n!}{s^{n + 1}}$
For B
We have to find Laplace transform of $c o s ω t$ . That is $L c o s ω t$

From the Laplace Table:

$L \cos a t = s / (s^{2} + a^{2})$

$L \cos ω t = s / (s^{2} + ω^{2})$

For C

We have to find Laplace transorm of $\sinh (c t)$ that is $L \sinh c t$

From the Laplace Table:

$L \sinh a t = a / (s^{2} + a^{2})$

It shows that:

$L \sinh c t = c / (s^{2} + c^{2})$

For D

We have to find Laplace transorm of $\cosh (c t)$ that is $L \cosh c t$

From the Laplace Table:

$L \cosh a t = s / (s^{2} + a^{2})$

It shows that:

$L \cosh c t = s / (s^{2} + c^{2})$

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