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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
t (s)f(t)t = 0.6f(0.6) = ?

Find the inverse Laplace transform f(t) of F(s) = 12/(s² + 4) with a table of transform pairs, and evaluate f(0.6).

F(s) = 12/(s² + 4)t = 0.6 s
f(0.6) =
2.Easy
t (s)f(t)f(0⁺) = ?

A signal f(t) has the Laplace transform F(s) = (5s² + 27s + 34)/(s(s + 2)(s + 4)). Use the initial value theorem to find f(0⁺), the value of f(t) just after t = 0.

F(s) = (5s² + 27s + 34)/(s(s + 2)(s + 4))
f(0⁺) =
3.Medium
t (s)f(t)t = 0.5f(0.5) = ?

Find f(t) for F(s) = (5s + 34)/(s² + 4s + 4) and evaluate f(0.5).

F(s) = (5s + 34)/(s² + 4s + 4)t = 0.5 s
f(0.5) =
4.Medium
t (s)f(t)t = 0.25f(0.25) = ?

Find f(t) for F(s) = (2s + 32)/(s² + 8s + 16) and evaluate f(0.25).

F(s) = (2s + 32)/(s² + 8s + 16)t = 0.25 s
f(0.25) =
5.Hard
t (s)y(t)t = 0.1y(0.1) = ?

A system obeys y″ + 11y′ + 30y = 15·u(t). It starts at rest (y(0) = 0, y′(0) = 0) and the input is a step u(t) = 10 for t ≥ 0. Use the Laplace transform to find the output y(0.1).

y″ + 11y′ + 30y = 15·u(t)u(t) = 10y(0) = 0, y′(0) = 0t = 0.1 s
y(0.1) =
6.Hard
t (s)y(t)t = 0.5y(0.5) = ?

A system obeys y″ + 6y′ + 8y = 48·u(t). It starts at rest (y(0) = 0, y′(0) = 0) and the input is a step u(t) = 5 for t ≥ 0. Use the Laplace transform to find the output y(0.5).

y″ + 6y′ + 8y = 48·u(t)u(t) = 5y(0) = 0, y′(0) = 0t = 0.5 s
y(0.5) =

Answer key

  1. 1. f(0.6) = 5.592
  2. 2. f(0⁺) = 5
  3. 3. f(0.5) = 6.254
  4. 4. f(0.25) = 2.943
  5. 5. y(0.1) = 0.5244
  6. 6. y(0.5) = 11.99

Full step-by-step solutions: practise this topic on examproblems.com.