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 = 0.75f(0.75) = ?

Find the inverse Laplace transform f(t) of F(s) = 10/(s + 2) + 7/s with a table of transform pairs, and evaluate f(0.75).

F(s) = 10/(s + 2) + 7/st = 0.75 s
f(0.75) =
2.Easy
t (s)f(t)

A signal f(t) has the Laplace transform F(s) = (2s + 37)/(s² + 5s + 6). Find the initial slope f′(0⁺) with the initial value theorem.

F(s) = (2s + 37)/(s² + 5s + 6)
f′(0⁺) =
3.Medium
ReIm−1−2−3−4−51

F(s) = 2/(s² + 9s + 20). Its inverse transform has the form f(t) = A·e−4t + B·e−5t. Find the coefficient A by partial fractions.

F(s) = 2/(s² + 9s + 20)
A =
4.Medium
t (s)f(t)t = 0.1f(0.1) = ?

Find f(t) for F(s) = (s + 10)/(s² + 10s + 25) and evaluate f(0.1).

F(s) = (s + 10)/(s² + 10s + 25)t = 0.1 s
f(0.1) =
5.Hard
t (s)y(t)t = 0.1y(0.1) = ?

Solve y″ + 11y′ + 30y = 0 with y(0) = 10 and y′(0) = 15 using the Laplace transform, and find y(0.1).

y″ + 11y′ + 30y = 0y(0) = 10y′(0) = 15t = 0.1 s
y(0.1) =
6.Hard
t (s)y(t)t = 1y(1) = ?

A system obeys y″ + 6y′ + 5y = 10·u(t), with y(0) = 4 and y′(0) = 0. At t = 0 a step input u(t) = 1 is applied. Use the Laplace transform to find y(1).

y″ + 6y′ + 5y = 10·u(t)y(0) = 4y′(0) = 0u(t) = 1t = 1 s
y(1) =

Answer key

  1. 1. f(0.75) = 9.231
  2. 2. f′(0⁺) = 27
  3. 3. A = 2
  4. 4. f(0.1) = 0.9098
  5. 5. y(0.1) = 9.817
  6. 6. y(1) = 2.916

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