The inverse Laplace transform of 1/s^2 is equal to t. In this post, we will learn how to find the inverse Laplace transform of 1 divided by s2.
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How to Find Inverse Laplace of 1/s2
To find the inverse Laplace transform of 1 by s square, we will use the formula of the Laplace transform of tn which is given by
L{tn} = $\dfrac{n!}{s^{n+1}}$ where n=0, 1, 2, 3, …
Now we take the inverse Laplace transform on both sides. By doing so, we get that
tn = L-1$\left(\dfrac{n!}{s^{n+1}} \right)$
This implies that
tn = n! L-1$\left(\dfrac{1}{s^{n+1}} \right)$
Put n=1 in the above formula in order to get the inverse Laplace transform of 1/s2. Thus, we obtain that
t1 = 1! L-1(1/s2)
⇒ t = L-1(1/s2).
Therefore, the inverse Laplace transform formula of 1/s^2 is equal to L-1(1/s2) = t, that is, t is the inverse Laplace of 1 by s^2.
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FAQs
Answer: The inverse Laplace transform of 1/s2 is t.
This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.