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(0⁺) = ?

A signal f(t) has the Laplace transform F(s) = (9s² + 8s + 49)/(s(s + 4)(s + 7)). Use the initial value theorem to find f(0⁺), the value of f(t) just after t = 0.

F(s) = (9s² + 8s + 49)/(s(s + 4)(s + 7))
f(0⁺) =
2.Easy
t (s)f(t)f(0⁺) = ?

A signal f(t) has the Laplace transform F(s) = (8s² + 19s + 5)/(s(s + 4)(s + 5)). Use the initial value theorem to find f(0⁺), the value of f(t) just after t = 0.

F(s) = (8s² + 19s + 5)/(s(s + 4)(s + 5))
f(0⁺) =
3.Medium
t (s)f(t)t = 0.25f(0.25) = ?

Find f(t) for F(s) = 45/(s(s + 2)(s + 4)) by partial fractions, and evaluate f(0.25).

F(s) = 45/(s(s + 2)(s + 4))t = 0.25 s
f(0.25) =
4.Medium
t (s)f(t)t = 0.6f(0.6) = ?

Find f(t) for F(s) = (s + 35)/(s² + 6s + 9) and evaluate f(0.6).

F(s) = (s + 35)/(s² + 6s + 9)t = 0.6 s
f(0.6) =
5.Hard
t (s)y(t)t = 1.2y(1.2) = ?

Solve y″ + 5y′ + 4y = 0 with y(0) = 1 and y′(0) = 10 using the Laplace transform, and find y(1.2).

y″ + 5y′ + 4y = 0y(0) = 1y′(0) = 10t = 1.2 s
y(1.2) =
6.Hard
t (s)y(t)t = 0.2y(0.2) = ?

Solve y″ + 11y′ + 30y = 0 with y(0) = 1 and y′(0) = 3 using the Laplace transform, and find y(0.2).

y″ + 11y′ + 30y = 0y(0) = 1y′(0) = 3t = 0.2 s
y(0.2) =

Answer key

  1. 1. f(0⁺) = 9
  2. 2. f(0⁺) = 8
  3. 3. f(0.25) = 0.8709
  4. 4. f(0.6) = 3.339
  5. 5. y(1.2) = 1.375
  6. 6. y(0.2) = 0.9014

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