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 = 0.25f(0.25) = ?

Find the inverse Laplace transform f(t) of F(s) = 13/(s² + 25) with a table of transform pairs, and evaluate f(0.25).

F(s) = 13/(s² + 25)t = 0.25 s
f(0.25) =
2.Easy
t (s)f(t)f(∞) = ?

A signal f(t) has the Laplace transform F(s) = 40/(s(s² + 2s + 11)). Use the final value theorem to find the value f(∞) that f(t) settles to.

F(s) = 40/(s(s² + 2s + 11))
f(∞) =
3.Medium
t (s)f(t)t = 1.5f(1.5) = ?

Find f(t) for F(s) = (2s + 20)/(s² + 2s + 1) and evaluate f(1.5).

F(s) = (2s + 20)/(s² + 2s + 1)t = 1.5 s
f(1.5) =
4.Medium
t (s)f(t)t = 1.2f(1.2) = ?

Find f(t) for F(s) = (4s + 2)/(s² + 2s + 1) and evaluate f(1.2).

F(s) = (4s + 2)/(s² + 2s + 1)t = 1.2 s
f(1.2) =
5.Hard
t (s)y(t)t = 0.25y(0.25) = ?

A system obeys y″ + 8y′ + 12y = 24·u(t), with y(0) = 5 and y′(0) = 0. At t = 0 a step input u(t) = 2 is applied. Use the Laplace transform to find y(0.25).

y″ + 8y′ + 12y = 24·u(t)y(0) = 5y′(0) = 0u(t) = 2t = 0.25 s
y(0.25) =
6.Hard
t (s)y(t)t = 0.1y(0.1) = ?

Solve y″ + 8y′ + 15y = 0 with y(0) = 10 and y′(0) = 5 using the Laplace transform, and find y(0.1).

y″ + 8y′ + 15y = 0y(0) = 10y′(0) = 5t = 0.1 s
y(0.1) =

Answer key

  1. 1. f(0.25) = 2.467
  2. 2. f(∞) = 3.636
  3. 3. f(1.5) = 6.471
  4. 4. f(1.2) = 0.4819
  5. 5. y(0.25) = 4.798
  6. 6. y(0.1) = 9.758

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