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 = 0.1f(0.1) = ?

Find the inverse Laplace transform f(t) of F(s) = 4s/(s² + 4) with a table of transform pairs, and evaluate f(0.1).

F(s) = 4s/(s² + 4)t = 0.1 s
f(0.1) =
2.Easy
t (s)f(t)t = 1f(1) = ?

Find the inverse Laplace transform f(t) of F(s) = 3s/(s² + 16) with a table of transform pairs, and evaluate f(1).

F(s) = 3s/(s² + 16)t = 1 s
f(1) =
3.Medium
t (s)f(t)t = 0.2f(0.2) = ?

Find f(t) for F(s) = (4s + 26)/(s² + 10s + 25) and evaluate f(0.2).

F(s) = (4s + 26)/(s² + 10s + 25)t = 0.2 s
f(0.2) =
4.Medium
ReIm−1−2−312

Find f(t) for F(s) = (2s + 6)/(s² + 4s + 8) by completing the square, and evaluate f(0.25).

F(s) = (2s + 6)/(s² + 4s + 8)t = 0.25 s
f(0.25) =
5.Hard
t (s)y(t)t = 0.3y(0.3) = ?

A system obeys y″ + 7y′ + 6y = 24·u(t), with y(0) = 3 and y′(0) = 0. At t = 0 a step input u(t) = 2 is applied. Use the Laplace transform to find y(0.3).

y″ + 7y′ + 6y = 24·u(t)y(0) = 3y′(0) = 0u(t) = 2t = 0.3 s
y(0.3) =
6.Hard
t (s)y(t)t = 0.75y(0.75) = ?

A system obeys y″ + 6y′ + 5y = 20·u(t). It starts at rest (y(0) = 0, y′(0) = 0) and the input is a step u(t) = 1 for t ≥ 0. Use the Laplace transform to find the output y(0.75).

y″ + 6y′ + 5y = 20·u(t)u(t) = 1y(0) = 0, y′(0) = 0t = 0.75 s
y(0.75) =

Answer key

  1. 1. f(0.1) = 3.92
  2. 2. f(1) = −1.961
  3. 3. f(0.2) = 1.913
  4. 4. f(0.25) = 1.355
  5. 5. y(0.3) = 3.72
  6. 6. y(0.75) = 1.662

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