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 = 0.1f(0.1) = ?

Find the inverse Laplace transform f(t) of F(s) = 19s/(s² + 9) with a table of transform pairs, and evaluate f(0.1).

F(s) = 19s/(s² + 9)t = 0.1 s
f(0.1) =
2.Easy
t (s)f(t)

A signal f(t) has the Laplace transform F(s) = (−5s + 15)/(s² + 6s + 26). Find the initial slope f′(0⁺) with the initial value theorem.

F(s) = (−5s + 15)/(s² + 6s + 26)
f′(0⁺) =
3.Medium
t (s)f(t)t = 0.6f(0.6) = ?

Find f(t) for F(s) = 35/(s(s + 1)(s + 5)) by partial fractions, and evaluate f(0.6).

F(s) = 35/(s(s + 1)(s + 5))t = 0.6 s
f(0.6) =
4.Medium
t (s)f(t)t = 0.2f(0.2) = ?

Find f(t) for F(s) = (3s + 19)/(s² + 8s + 16) and evaluate f(0.2).

F(s) = (3s + 19)/(s² + 8s + 16)t = 0.2 s
f(0.2) =
5.Hard
t (s)y(t)t = 0.2y(0.2) = ?

Solve y″ + 11y′ + 30y = 0 with y(0) = 8 and y′(0) = −4 using the Laplace transform, and find y(0.2).

y″ + 11y′ + 30y = 0y(0) = 8y′(0) = −4t = 0.2 s
y(0.2) =
6.Hard
t (s)y(t)t = 0.2y(0.2) = ?

A system obeys y″ + 5y′ + 4y = 4·u(t), with y(0) = 5 and y′(0) = 0. At t = 0 a step input u(t) = 2 is applied. Use the Laplace transform to find y(0.2).

y″ + 5y′ + 4y = 4·u(t)y(0) = 5y′(0) = 0u(t) = 2t = 0.2 s
y(0.2) =

Answer key

  1. 1. f(0.1) = 18.15
  2. 2. f′(0⁺) = 45
  3. 3. f(0.6) = 2.285
  4. 4. f(0.2) = 1.977
  5. 5. y(0.2) = 5.344
  6. 6. y(0.2) = 4.826

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