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) = 2s/(s² + 4) with a table of transform pairs, and evaluate f(1.2).

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

A signal f(t) has the Laplace transform F(s) = (5s + 9)/(s² + 7s + 17). Find the initial slope f′(0⁺) with the initial value theorem.

F(s) = (5s + 9)/(s² + 7s + 17)
f′(0⁺) =
3.Medium
t (s)f(t)t = 0.1f(0.1) = ?

Find f(t) for F(s) = 40/(s(s + 3)(s + 6)) by partial fractions, and evaluate f(0.1).

F(s) = 40/(s(s + 3)(s + 6))t = 0.1 s
f(0.1) =
4.Medium
t (s)f(t)t = 0.4f(0.4) = ?

Find f(t) for F(s) = (5s + 38)/(s² + 4s + 4) and evaluate f(0.4).

F(s) = (5s + 38)/(s² + 4s + 4)t = 0.4 s
f(0.4) =
5.Hard
t (s)y(t)t = 0.5y(0.5) = ?

A system obeys y″ + 5y′ + 4y = 12·u(t), with y(0) = 5 and y′(0) = 0. At t = 0 a step input u(t) = 10 is applied. Use the Laplace transform to find y(0.5).

y″ + 5y′ + 4y = 12·u(t)y(0) = 5y′(0) = 0u(t) = 10t = 0.5 s
y(0.5) =
6.Hard
t (s)y(t)t = 0.8y(0.8) = ?

A system obeys y″ + 4y′ + 3y = 3·u(t), with y(0) = 4 and y′(0) = 0. At t = 0 a step input u(t) = 10 is applied. Use the Laplace transform to find y(0.8).

y″ + 4y′ + 3y = 3·u(t)y(0) = 4y′(0) = 0u(t) = 10t = 0.8 s
y(0.8) =

Answer key

  1. 1. f(1.2) = −1.475
  2. 2. f′(0⁺) = −26
  3. 3. f(0.1) = 0.1493
  4. 4. f(0.4) = 7.279
  5. 5. y(0.5) = 10.91
  6. 6. y(0.8) = 6.228

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