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)f(∞) = ?

A signal f(t) has the Laplace transform F(s) = 12(s + 5)/(s(s + 4)(s + 6)). Use the final value theorem to find the value f(∞) that f(t) settles to.

F(s) = 12(s + 5)/(s(s + 4)(s + 6))
f(∞) =
2.Easy
t (s)f(t)

A signal f(t) has the Laplace transform F(s) = (5s + 37)/(s² + 5s + 3). Find the initial slope f′(0⁺) with the initial value theorem.

F(s) = (5s + 37)/(s² + 5s + 3)
f′(0⁺) =
3.Medium
t (s)f(t)t = 0.2f(0.2) = ?

Find f(t) for F(s) = (3s + 35)/(s² + 4s + 4) and evaluate f(0.2).

F(s) = (3s + 35)/(s² + 4s + 4)t = 0.2 s
f(0.2) =
4.Medium
t (s)f(t)t = 0.6f(0.6) = ?

Find f(t) for F(s) = (5s + 13)/(s² + 6s + 9) and evaluate f(0.6).

F(s) = (5s + 13)/(s² + 6s + 9)t = 0.6 s
f(0.6) =
5.Hard
t (s)y(t)t = 0.2y(0.2) = ?

Solve y″ + 11y′ + 30y = 0 with y(0) = 7 and y′(0) = 13 using the Laplace transform, and find y(0.2).

y″ + 11y′ + 30y = 0y(0) = 7y′(0) = 13t = 0.2 s
y(0.2) =
6.Hard
t (s)y(t)t = 0.6y(0.6) = ?

Solve y″ + 5y′ + 6y = 0 with y(0) = 6 and y′(0) = 6 using the Laplace transform, and find y(0.6).

y″ + 5y′ + 6y = 0y(0) = 6y′(0) = 6t = 0.6 s
y(0.6) =

Answer key

  1. 1. f(∞) = 2.5
  2. 2. f′(0⁺) = 12
  3. 3. f(0.2) = 5.899
  4. 4. f(0.6) = 0.6281
  5. 5. y(0.2) = 5.776
  6. 6. y(0.6) = 4.253

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