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) = 10/(s + 3)² with a table of transform pairs, and evaluate f(0.25).

F(s) = 10/(s + 3)²t = 0.25 s
f(0.25) =
2.Easy
t (s)f(t)f(∞) = ?

A signal f(t) has the Laplace transform F(s) = 20/(s(s² + 6s + 10)). Use the final value theorem to find the value f(∞) that f(t) settles to.

F(s) = 20/(s(s² + 6s + 10))
f(∞) =
3.Medium
t (s)f(t)t = 0.3f(0.3) = ?

Find f(t) for F(s) = 55/(s(s + 5)(s + 6)) by partial fractions, and evaluate f(0.3).

F(s) = 55/(s(s + 5)(s + 6))t = 0.3 s
f(0.3) =
4.Medium
ReIm−1−2−3−4−5−6−7−8−91

F(s) = 38/(s² + 11s + 24). Its inverse transform has the form f(t) = A·e−3t + B·e−8t. Find the coefficient A by partial fractions.

F(s) = 38/(s² + 11s + 24)
A =
5.Hard
t (s)y(t)t = 0.3y(0.3) = ?

Solve y″ + 7y′ + 12y = 0 with y(0) = 5 and y′(0) = −8 using the Laplace transform, and find y(0.3).

y″ + 7y′ + 12y = 0y(0) = 5y′(0) = −8t = 0.3 s
y(0.3) =
6.Hard
t (s)y(t)t = 0.3y(0.3) = ?

A system obeys y″ + 7y′ + 12y = 36·u(t), with y(0) = 1 and y′(0) = 0. At t = 0 a step input u(t) = 10 is applied. Use the Laplace transform to find y(0.3).

y″ + 7y′ + 12y = 36·u(t)y(0) = 1y′(0) = 0u(t) = 10t = 0.3 s
y(0.3) =

Answer key

  1. 1. f(0.25) = 1.181
  2. 2. f(∞) = 2
  3. 3. f(0.3) = 0.8941
  4. 4. A = 7.6
  5. 5. y(0.3) = 2.77
  6. 6. y(0.3) = 9.042

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