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)f(∞) = ?

A signal f(t) has the Laplace transform F(s) = 38/(s(s² + 8s + 12)). Use the final value theorem to find the value f(∞) that f(t) settles to.

F(s) = 38/(s(s² + 8s + 12))
f(∞) =
2.Easy
t (s)f(t)t = 0.3f(0.3) = ?

Find the inverse Laplace transform f(t) of F(s) = 12/(s + 4) − 5/s with a table of transform pairs, and evaluate f(0.3).

F(s) = 12/(s + 4) − 5/st = 0.3 s
f(0.3) =
3.Medium
t (s)f(t)t = 0.75f(0.75) = ?

Find f(t) for F(s) = 30/(s(s + 1)(s + 3)) by partial fractions, and evaluate f(0.75).

F(s) = 30/(s(s + 1)(s + 3))t = 0.75 s
f(0.75) =
4.Medium
t (s)f(t)t = 0.1f(0.1) = ?

Find f(t) for F(s) = (5s + 33)/(s² + 10s + 25) and evaluate f(0.1).

F(s) = (5s + 33)/(s² + 10s + 25)t = 0.1 s
f(0.1) =
5.Hard
t (s)y(t)t = 0.3y(0.3) = ?

A system obeys y″ + 9y′ + 20y = 80·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(0.3).

y″ + 9y′ + 20y = 80·u(t)y(0) = 1y′(0) = 0u(t) = 5t = 0.3 s
y(0.3) =
6.Hard
t (s)y(t)t = 0.2y(0.2) = ?

A system obeys y″ + 6y′ + 5y = 10·u(t), with y(0) = 2 and y′(0) = 0. At t = 0 a step input u(t) = 1 is applied. Use the Laplace transform to find y(0.2).

y″ + 6y′ + 5y = 10·u(t)y(0) = 2y′(0) = 0u(t) = 1t = 0.2 s
y(0.2) =

Answer key

  1. 1. f(∞) = 3.167
  2. 2. f(0.3) = −1.386
  3. 3. f(0.75) = 3.441
  4. 4. f(0.1) = 3.518
  5. 5. y(0.3) = 8.344
  6. 6. y(0.2) = 2

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