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 = 0.2f(0.2) = ?

Find the inverse Laplace transform f(t) of F(s) = 14s/(s² + 36) with a table of transform pairs, and evaluate f(0.2).

F(s) = 14s/(s² + 36)t = 0.2 s
f(0.2) =
2.Easy
t (s)f(t)

A signal f(t) has the Laplace transform F(s) = (8s + 9)/(s² + 6s + 14). Find the initial slope f′(0⁺) with the initial value theorem.

F(s) = (8s + 9)/(s² + 6s + 14)
f′(0⁺) =
3.Medium
t (s)f(t)t = 0.2f(0.2) = ?

Find f(t) for F(s) = 55/(s(s + 2)(s + 5)) by partial fractions, and evaluate f(0.2).

F(s) = 55/(s(s + 2)(s + 5))t = 0.2 s
f(0.2) =
4.Medium
t (s)f(t)t = 0.25f(0.25) = ?

Find f(t) for F(s) = (6s + 24)/(s² + 4s + 4) and evaluate f(0.25).

F(s) = (6s + 24)/(s² + 4s + 4)t = 0.25 s
f(0.25) =
5.Hard
t (s)y(t)t = 0.2y(0.2) = ?

A system obeys y″ + 10y′ + 24y = 72·u(t), with y(0) = 3 and y′(0) = 0. At t = 0 a step input u(t) = 10 is applied. Use the Laplace transform to find y(0.2).

y″ + 10y′ + 24y = 72·u(t)y(0) = 3y′(0) = 0u(t) = 10t = 0.2 s
y(0.2) =
6.Hard
t (s)y(t)t = 0.1y(0.1) = ?

A system obeys y″ + 5y′ + 6y = 6·u(t), with y(0) = 5 and y′(0) = 0. At t = 0 a step input u(t) = 2 is applied. Use the Laplace transform to find y(0.1).

y″ + 5y′ + 6y = 6·u(t)y(0) = 5y′(0) = 0u(t) = 2t = 0.1 s
y(0.1) =

Answer key

  1. 1. f(0.2) = 5.073
  2. 2. f′(0⁺) = −39
  3. 3. f(0.2) = 0.7043
  4. 4. f(0.25) = 5.459
  5. 5. y(0.2) = 9.869
  6. 6. y(0.1) = 4.924

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