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) = (−7s + 5)/(s² + 3s + 3). Find the initial slope f′(0⁺) with the initial value theorem.

F(s) = (−7s + 5)/(s² + 3s + 3)
f′(0⁺) =
2.Easy
t (s)f(t)f(∞) = ?

A signal f(t) has the Laplace transform F(s) = 5/(s(s² + 4s + 12)). Use the final value theorem to find the value f(∞) that f(t) settles to.

F(s) = 5/(s(s² + 4s + 12))
f(∞) =
3.Medium
t (s)f(t)t = 0.1f(0.1) = ?

Find f(t) for F(s) = 50/(s(s + 4)(s + 5)) by partial fractions, and evaluate f(0.1).

F(s) = 50/(s(s + 4)(s + 5))t = 0.1 s
f(0.1) =
4.Medium
t (s)f(t)t = 0.1f(0.1) = ?

Find f(t) for F(s) = (6s + 26)/(s² + 8s + 16) and evaluate f(0.1).

F(s) = (6s + 26)/(s² + 8s + 16)t = 0.1 s
f(0.1) =
5.Hard
ReIm−224

A system is described by the differential equation y″ + 6y′ + 25y = 9u, with input u(t) and output y(t). Find its transfer function G(s) = Y(s)/U(s) (zero initial conditions) and evaluate the impulse response g(t) at t = 0.4 s. Find g(0.4).

y″ + 6y′ + 25y = 9ut = 0.4 s
g(0.4) =
6.Hard
t (s)y(t)t = 0.6y(0.6) = ?

A system obeys y″ + 5y′ + 6y = 12·u(t), with y(0) = 3 and y′(0) = 0. At t = 0 a step input u(t) = 1 is applied. Use the Laplace transform to find y(0.6).

y″ + 5y′ + 6y = 12·u(t)y(0) = 3y′(0) = 0u(t) = 1t = 0.6 s
y(0.6) =

Answer key

  1. 1. f′(0⁺) = 26
  2. 2. f(∞) = 0.4167
  3. 3. f(0.1) = 0.1863
  4. 4. f(0.1) = 4.156
  5. 5. g(0.4) = 0.6774
  6. 6. y(0.6) = 2.573

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