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 = 0.4f(0.4) = ?

Find the inverse Laplace transform f(t) of F(s) = 2/(s + 5)² with a table of transform pairs, and evaluate f(0.4).

F(s) = 2/(s + 5)²t = 0.4 s
f(0.4) =
2.Easy
t (s)f(t)t = 1.2f(1.2) = ?

Find the inverse Laplace transform f(t) of F(s) = 8s/(s² + 36) with a table of transform pairs, and evaluate f(1.2).

F(s) = 8s/(s² + 36)t = 1.2 s
f(1.2) =
3.Medium
ReIm−1−2−3−4−5−6−7−81

F(s) = 23/(s² + 12s + 35). Its inverse transform has the form f(t) = A·e−5t + B·e−7t. Find the coefficient A by partial fractions.

F(s) = 23/(s² + 12s + 35)
A =
4.Medium
t (s)f(t)t = 0.8f(0.8) = ?

Find f(t) for F(s) = (s + 5)/(s² + 2s + 1) and evaluate f(0.8).

F(s) = (s + 5)/(s² + 2s + 1)t = 0.8 s
f(0.8) =
5.Hard
t (s)y(t)t = 0.3y(0.3) = ?

Solve y″ + 9y′ + 18y = 0 with y(0) = 9 and y′(0) = −11 using the Laplace transform, and find y(0.3).

y″ + 9y′ + 18y = 0y(0) = 9y′(0) = −11t = 0.3 s
y(0.3) =
6.Hard
t (s)y(t)t = 0.2y(0.2) = ?

A system obeys y″ + 11y′ + 30y = 90·u(t), with y(0) = 2 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″ + 11y′ + 30y = 90·u(t)y(0) = 2y′(0) = 0u(t) = 10t = 0.2 s
y(0.2) =

Answer key

  1. 1. f(0.4) = 0.1083
  2. 2. f(1.2) = 4.867
  3. 3. A = 11.5
  4. 4. f(0.8) = 1.887
  5. 5. y(0.3) = 4.946
  6. 6. y(0.2) = 10.36

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