Inverse Laplace Transform Practice Problems and Step-by-Step Solutions

Published on April 1, 2026

Calculus

This set of exercises focuses on finding the inverse Laplace transforms of various rational and exponential functions, including the use of partial fraction decomposition and shifting theorems.

Question

Answer

Here are the solutions for the problems presented in the image.

Section 3

11. Find

:
Using the property

, we multiply and divide by 3:

12. Find

:
Using the property

with

13. Find

:
Using the frequency shifting theorem

and

14. Find

:
Complete the square:

15. Find

:
Using the shifting theorem

Section 4

16.

17.

18.

19.

Section 5

20.

21.

22.

Section 6

23.

. Applying shift theorem

24.

25.

26.

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