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)t = 1.2f(1.2) = ?

Find the inverse Laplace transform f(t) of F(s) = 12s/(s² + 4) with a table of transform pairs, and evaluate f(1.2).

F(s) = 12s/(s² + 4)t = 1.2 s
f(1.2) =
2.Easy
t (s)f(t)f(0⁺) = ?

A signal f(t) has the Laplace transform F(s) = (−6s² + 14s + 34)/(s(s + 2)(s + 6)). Use the initial value theorem to find f(0⁺), the value of f(t) just after t = 0.

F(s) = (−6s² + 14s + 34)/(s(s + 2)(s + 6))
f(0⁺) =
3.Medium
t (s)f(t)t = 0.4f(0.4) = ?

Find f(t) for F(s) = 10/(s(s + 2)(s + 4)) by partial fractions, and evaluate f(0.4).

F(s) = 10/(s(s + 2)(s + 4))t = 0.4 s
f(0.4) =
4.Medium
t (s)f(t)t = 0.25f(0.25) = ?

Find f(t) for F(s) = 30/(s(s + 4)(s + 6)) by partial fractions, and evaluate f(0.25).

F(s) = 30/(s(s + 4)(s + 6))t = 0.25 s
f(0.25) =
5.Hard
t (s)y(t)t = 0.2y(0.2) = ?

A system obeys y″ + 11y′ + 30y = 90·u(t), with y(0) = 1 and y′(0) = 0. At t = 0 a step input u(t) = 5 is applied. Use the Laplace transform to find y(0.2).

y″ + 11y′ + 30y = 90·u(t)y(0) = 1y′(0) = 0u(t) = 5t = 0.2 s
y(0.2) =
6.Hard
t (s)y(t)t = 0.2y(0.2) = ?

Solve y″ + 5y′ + 4y = 0 with y(0) = 5 and y′(0) = −2 using the Laplace transform, and find y(0.2).

y″ + 5y′ + 4y = 0y(0) = 5y′(0) = −2t = 0.2 s
y(0.2) =

Answer key

  1. 1. f(1.2) = −8.849
  2. 2. f(0⁺) = −6
  3. 3. f(0.4) = 0.379
  4. 4. f(0.25) = 0.4283
  5. 5. y(0.2) = 5.182
  6. 6. y(0.2) = 4.463

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