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 = 0.5f(0.5) = ?

Find the inverse Laplace transform f(t) of F(s) = 10/(s² + 16) with a table of transform pairs, and evaluate f(0.5).

F(s) = 10/(s² + 16)t = 0.5 s
f(0.5) =
2.Easy
t (s)f(t)t = 0.2f(0.2) = ?

Find the inverse Laplace transform f(t) of F(s) = 7/(s + 2)² with a table of transform pairs, and evaluate f(0.2).

F(s) = 7/(s + 2)²t = 0.2 s
f(0.2) =
3.Medium
t (s)f(t)t = 0.3f(0.3) = ?

Find f(t) for F(s) = (3s + 2)/(s² + 6s + 9) and evaluate f(0.3).

F(s) = (3s + 2)/(s² + 6s + 9)t = 0.3 s
f(0.3) =
4.Medium
t (s)f(t)t = 0.25f(0.25) = ?

Find f(t) for F(s) = 60/(s(s + 3)(s + 4)) by partial fractions, and evaluate f(0.25).

F(s) = 60/(s(s + 3)(s + 4))t = 0.25 s
f(0.25) =
5.Hard
t (s)y(t)t = 0.25y(0.25) = ?

Solve y″ + 5y′ + 6y = 0 with y(0) = 8 and y′(0) = −5 using the Laplace transform, and find y(0.25).

y″ + 5y′ + 6y = 0y(0) = 8y′(0) = −5t = 0.25 s
y(0.25) =
6.Hard
t (s)y(t)t = 0.4y(0.4) = ?

Solve y″ + 6y′ + 8y = 0 with y(0) = −7 and y′(0) = 11 using the Laplace transform, and find y(0.4).

y″ + 6y′ + 8y = 0y(0) = −7y′(0) = 11t = 0.4 s
y(0.4) =

Answer key

  1. 1. f(0.5) = 2.273
  2. 2. f(0.2) = 0.9384
  3. 3. f(0.3) = 0.3659
  4. 4. f(0.25) = 1.071
  5. 5. y(0.25) = 6.328
  6. 6. y(0.4) = −3.516

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