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) = 17/(s + 3)² with a table of transform pairs, and evaluate f(0.4).

F(s) = 17/(s + 3)²t = 0.4 s
f(0.4) =
2.Easy
t (s)f(t)f(∞) = ?

A signal f(t) has the Laplace transform F(s) = 19(s + 4)/(s(s + 3)(s + 8)). Use the final value theorem to find the value f(∞) that f(t) settles to.

F(s) = 19(s + 4)/(s(s + 3)(s + 8))
f(∞) =
3.Medium
t (s)f(t)t = 0.2f(0.2) = ?

Find f(t) for F(s) = 55/(s(s + 5)(s + 6)) by partial fractions, and evaluate f(0.2).

F(s) = 55/(s(s + 5)(s + 6))t = 0.2 s
f(0.2) =
4.Medium
t (s)f(t)t = 0.6f(0.6) = ?

Find f(t) for F(s) = (6s + 8)/(s² + 2s + 1) and evaluate f(0.6).

F(s) = (6s + 8)/(s² + 2s + 1)t = 0.6 s
f(0.6) =
5.Hard
t (s)y(t)t = 0.75y(0.75) = ?

Solve y″ + 6y′ + 5y = 0 with y(0) = 8 and y′(0) = −3 using the Laplace transform, and find y(0.75).

y″ + 6y′ + 5y = 0y(0) = 8y′(0) = −3t = 0.75 s
y(0.75) =
6.Hard
ReIm−1−2−3−4−5−61

A system is described by the differential equation y″ + 10y′ + 24y = 3u′ + 4u, with input u(t) and output y(t). Find its transfer function G(s) = Y(s)/U(s) (zero initial conditions) and evaluate the impulse response g(t) at t = 0.2 s. Find g(0.2).

y″ + 10y′ + 24y = 3u′ + 4ut = 0.2 s
g(0.2) =

Answer key

  1. 1. f(0.4) = 2.048
  2. 2. f(∞) = 3.167
  3. 3. f(0.2) = 0.5476
  4. 4. f(0.6) = 3.951
  5. 5. y(0.75) = 4.34
  6. 6. g(0.2) = 0.311

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