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 = 0.3f(0.3) = ?

Find the inverse Laplace transform f(t) of F(s) = 9/(s + 3) − 10/s with a table of transform pairs, and evaluate f(0.3).

F(s) = 9/(s + 3) − 10/st = 0.3 s
f(0.3) =
2.Easy
t (s)f(t)f(0⁺) = ?

A signal f(t) has the Laplace transform F(s) = (−8s + 26)/(s² + 10s + 16). Use the initial value theorem to find f(0⁺), the value of f(t) just after t = 0.

F(s) = (−8s + 26)/(s² + 10s + 16)
f(0⁺) =
3.Medium
t (s)f(t)t = 0.1f(0.1) = ?

Find f(t) for F(s) = (s + 19)/(s² + 10s + 25) and evaluate f(0.1).

F(s) = (s + 19)/(s² + 10s + 25)t = 0.1 s
f(0.1) =
4.Medium
t (s)f(t)t = 0.5f(0.5) = ?

Find f(t) for F(s) = 15/(s(s + 1)(s + 6)) by partial fractions, and evaluate f(0.5).

F(s) = 15/(s(s + 1)(s + 6))t = 0.5 s
f(0.5) =
5.Hard
t (s)y(t)t = 1y(1) = ?

Solve y″ + 4y′ + 3y = 0 with y(0) = 4 and y′(0) = 15 using the Laplace transform, and find y(1).

y″ + 4y′ + 3y = 0y(0) = 4y′(0) = 15t = 1 s
y(1) =
6.Hard
t (s)y(t)t = 0.1y(0.1) = ?

A system obeys y″ + 9y′ + 18y = 36·u(t), with y(0) = 5 and y′(0) = 0. At t = 0 a step input u(t) = 5 is applied. Use the Laplace transform to find y(0.1).

y″ + 9y′ + 18y = 36·u(t)y(0) = 5y′(0) = 0u(t) = 5t = 0.1 s
y(0.1) =

Answer key

  1. 1. f(0.3) = −6.341
  2. 2. f(0⁺) = −8
  3. 3. f(0.1) = 1.456
  4. 4. f(0.5) = 0.7053
  5. 5. y(1) = 4.493
  6. 6. y(0.1) = 5.336

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