Laplace transforms worksheet with answers

Free printable Laplace transforms worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
t (s)f(t)t = 0.4f(0.4) = ?

Find the inverse Laplace transform f(t) of F(s) = 14s/(s² + 25) with a table of transform pairs, and evaluate f(0.4).

F(s) = 14s/(s² + 25)t = 0.4 s
f(0.4) =
2.Easy
t (s)f(t)

A signal f(t) has the Laplace transform F(s) = (−s + 19)/(s² + 5s + 29). Find the initial slope f′(0⁺) with the initial value theorem.

F(s) = (−s + 19)/(s² + 5s + 29)
f′(0⁺) =
3.Medium
t (s)f(t)t = 0.75f(0.75) = ?

Find f(t) for F(s) = 20/(s(s + 2)(s + 3)) by partial fractions, and evaluate f(0.75).

F(s) = 20/(s(s + 2)(s + 3))t = 0.75 s
f(0.75) =
4.Medium
t (s)f(t)t = 0.5f(0.5) = ?

Find f(t) for F(s) = 20/(s(s + 3)(s + 5)) by partial fractions, and evaluate f(0.5).

F(s) = 20/(s(s + 3)(s + 5))t = 0.5 s
f(0.5) =
5.Hard
t (s)y(t)t = 0.2y(0.2) = ?

Solve y″ + 8y′ + 15y = 0 with y(0) = −5 and y′(0) = −13 using the Laplace transform, and find y(0.2).

y″ + 8y′ + 15y = 0y(0) = −5y′(0) = −13t = 0.2 s
y(0.2) =
6.Hard
t (s)y(t)t = 0.5y(0.5) = ?

Solve y″ + 6y′ + 5y = 0 with y(0) = 3 and y′(0) = 13 using the Laplace transform, and find y(0.5).

y″ + 6y′ + 5y = 0y(0) = 3y′(0) = 13t = 0.5 s
y(0.5) =

Answer key

  1. 1. f(0.4) = −5.826
  2. 2. f′(0⁺) = 24
  3. 3. f(0.75) = 1.805
  4. 4. f(0.5) = 0.7537
  5. 5. y(0.2) = −5.277
  6. 6. y(0.5) = 3.917

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