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 = 0.75f(0.75) = ?

Find the inverse Laplace transform f(t) of F(s) = 8/(s² + 9) with a table of transform pairs, and evaluate f(0.75).

F(s) = 8/(s² + 9)t = 0.75 s
f(0.75) =
2.Easy
t (s)f(t)f(∞) = ?

A signal f(t) has the Laplace transform F(s) = 26/(s(s² + 3s + 19)). Use the final value theorem to find the value f(∞) that f(t) settles to.

F(s) = 26/(s(s² + 3s + 19))
f(∞) =
3.Medium
t (s)f(t)t = 0.8f(0.8) = ?

Find f(t) for F(s) = (3s + 23)/(s² + 2s + 1) and evaluate f(0.8).

F(s) = (3s + 23)/(s² + 2s + 1)t = 0.8 s
f(0.8) =
4.Medium
t (s)f(t)t = 0.75f(0.75) = ?

Find f(t) for F(s) = (2s + 5)/(s² + 2s + 1) and evaluate f(0.75).

F(s) = (2s + 5)/(s² + 2s + 1)t = 0.75 s
f(0.75) =
5.Hard
t (s)y(t)t = 0.1y(0.1) = ?

A system obeys y″ + 7y′ + 10y = 30·u(t), with y(0) = 1 and y′(0) = 0. At t = 0 a step input u(t) = 2 is applied. Use the Laplace transform to find y(0.1).

y″ + 7y′ + 10y = 30·u(t)y(0) = 1y′(0) = 0u(t) = 2t = 0.1 s
y(0.1) =
6.Hard
t (s)y(t)t = 0.3y(0.3) = ?

Solve y″ + 8y′ + 12y = 0 with y(0) = 7 and y′(0) = −3 using the Laplace transform, and find y(0.3).

y″ + 8y′ + 12y = 0y(0) = 7y′(0) = −3t = 0.3 s
y(0.3) =

Answer key

  1. 1. f(0.75) = 2.075
  2. 2. f(∞) = 1.368
  3. 3. f(0.8) = 8.537
  4. 4. f(0.75) = 2.008
  5. 5. y(0.1) = 1.199
  6. 6. y(0.3) = 4.896

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