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 = 0.3f(0.3) = ?

Find the inverse Laplace transform f(t) of F(s) = 15/(s + 3)² with a table of transform pairs, and evaluate f(0.3).

F(s) = 15/(s + 3)²t = 0.3 s
f(0.3) =
2.Easy
t (s)f(t)f(0⁺) = ?

A signal f(t) has the Laplace transform F(s) = (8s² + 20s + 24)/(s(s + 5)(s + 6)). Use the initial value theorem to find f(0⁺), the value of f(t) just after t = 0.

F(s) = (8s² + 20s + 24)/(s(s + 5)(s + 6))
f(0⁺) =
3.Medium
ReIm−2−4−6−8−10

F(s) = (4s + 40)/(s² + 6s + 5). Its inverse transform has the form f(t) = A·e−t + B·e−5t. Find the coefficient A by partial fractions.

F(s) = (4s + 40)/(s² + 6s + 5)
A =
4.Medium
t (s)f(t)t = 1f(1) = ?

Find f(t) for F(s) = 50/(s(s + 1)(s + 6)) by partial fractions, and evaluate f(1).

F(s) = 50/(s(s + 1)(s + 6))t = 1 s
f(1) =
5.Hard
t (s)y(t)t = 0.1y(0.1) = ?

A system obeys y″ + 9y′ + 18y = 36·u(t). It starts at rest (y(0) = 0, y′(0) = 0) and the input is a step u(t) = 1 for t ≥ 0. Use the Laplace transform to find the output y(0.1).

y″ + 9y′ + 18y = 36·u(t)u(t) = 1y(0) = 0, y′(0) = 0t = 0.1 s
y(0.1) =
6.Hard
t (s)y(t)t = 0.1y(0.1) = ?

A system obeys y″ + 9y′ + 18y = 18·u(t). It starts at rest (y(0) = 0, y′(0) = 0) and the input is a step u(t) = 2 for t ≥ 0. Use the Laplace transform to find the output y(0.1).

y″ + 9y′ + 18y = 18·u(t)u(t) = 2y(0) = 0, y′(0) = 0t = 0.1 s
y(0.1) =

Answer key

  1. 1. f(0.3) = 1.83
  2. 2. f(0⁺) = 8
  3. 3. A = 9
  4. 4. f(1) = 4.659
  5. 5. y(0.1) = 0.1344
  6. 6. y(0.1) = 0.1344

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