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)

A signal f(t) has the Laplace transform F(s) = (6s + 4)/(s² + 7s + 5). Find the initial slope f′(0⁺) with the initial value theorem.

F(s) = (6s + 4)/(s² + 7s + 5)
f′(0⁺) =
2.Easy
t (s)f(t)f(∞) = ?

A signal f(t) has the Laplace transform F(s) = 19/(s(s² + 6s + 24)). Use the final value theorem to find the value f(∞) that f(t) settles to.

F(s) = 19/(s(s² + 6s + 24))
f(∞) =
3.Medium
ReIm−1−2−3−4−5−61

F(s) = (5s + 30)/(s² + 9s + 20). Its inverse transform has the form f(t) = A·e−4t + B·e−5t. Find the coefficient A by partial fractions.

F(s) = (5s + 30)/(s² + 9s + 20)
A =
4.Medium
t (s)f(t)t = 0.4f(0.4) = ?

Find f(t) for F(s) = (4s + 38)/(s² + 10s + 25) and evaluate f(0.4).

F(s) = (4s + 38)/(s² + 10s + 25)t = 0.4 s
f(0.4) =
5.Hard
t (s)y(t)t = 0.6y(0.6) = ?

Solve y″ + 5y′ + 6y = 0 with y(0) = 9 and y′(0) = 15 using the Laplace transform, and find y(0.6).

y″ + 5y′ + 6y = 0y(0) = 9y′(0) = 15t = 0.6 s
y(0.6) =
6.Hard
t (s)y(t)t = 0.4y(0.4) = ?

A system obeys y″ + 7y′ + 10y = 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(0.4).

y″ + 7y′ + 10y = 15·u(t)u(t) = 10y(0) = 0, y′(0) = 0t = 0.4 s
y(0.4) =

Answer key

  1. 1. f′(0⁺) = −38
  2. 2. f(∞) = 0.7917
  3. 3. A = 10
  4. 4. f(0.4) = 1.516
  5. 5. y(0.6) = 7.195
  6. 6. y(0.4) = 5.12

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