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) = 7/(s + 4) − 4/s with a table of transform pairs, and evaluate f(0.2).

F(s) = 7/(s + 4) − 4/st = 0.2 s
f(0.2) =
2.Easy
t (s)f(t)f(∞) = ?

A signal f(t) has the Laplace transform F(s) = 17/(s(s² + 3s + 13)). Use the final value theorem to find the value f(∞) that f(t) settles to.

F(s) = 17/(s(s² + 3s + 13))
f(∞) =
3.Medium
t (s)f(t)t = 0.2f(0.2) = ?

Find f(t) for F(s) = (2s + 3)/(s² + 6s + 9) and evaluate f(0.2).

F(s) = (2s + 3)/(s² + 6s + 9)t = 0.2 s
f(0.2) =
4.Medium
ReIm−55

Find f(t) for F(s) = (5s + 30)/(s² + 4s + 40) by completing the square, and evaluate f(0.5).

F(s) = (5s + 30)/(s² + 4s + 40)t = 0.5 s
f(0.5) =
5.Hard
t (s)y(t)t = 0.5y(0.5) = ?

Solve y″ + 7y′ + 10y = 0 with y(0) = 10 and y′(0) = −4 using the Laplace transform, and find y(0.5).

y″ + 7y′ + 10y = 0y(0) = 10y′(0) = −4t = 0.5 s
y(0.5) =
6.Hard
t (s)y(t)t = 0.1y(0.1) = ?

A system obeys y″ + 9y′ + 20y = 120·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(0.1).

y″ + 9y′ + 20y = 120·u(t)u(t) = 1y(0) = 0, y′(0) = 0t = 0.1 s
y(0.1) =

Answer key

  1. 1. f(0.2) = −0.8547
  2. 2. f(∞) = 1.308
  3. 3. f(0.2) = 0.7683
  4. 4. f(0.5) = −1.648
  5. 5. y(0.5) = 5.203
  6. 6. y(0.1) = 0.4471

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