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 = 0.3f(0.3) = ?

Find the inverse Laplace transform f(t) of F(s) = 2/(s + 3) − 6/s with a table of transform pairs, and evaluate f(0.3).

F(s) = 2/(s + 3) − 6/st = 0.3 s
f(0.3) =
2.Easy
t (s)f(t)

A signal f(t) has the Laplace transform F(s) = (8s + 19)/(s² + 5s + 20). Find the initial slope f′(0⁺) with the initial value theorem.

F(s) = (8s + 19)/(s² + 5s + 20)
f′(0⁺) =
3.Medium
t (s)f(t)t = 0.4f(0.4) = ?

Find f(t) for F(s) = (5s + 9)/(s² + 2s + 1) and evaluate f(0.4).

F(s) = (5s + 9)/(s² + 2s + 1)t = 0.4 s
f(0.4) =
4.Medium
t (s)f(t)t = 0.3f(0.3) = ?

Find f(t) for F(s) = (s + 38)/(s² + 4s + 4) and evaluate f(0.3).

F(s) = (s + 38)/(s² + 4s + 4)t = 0.3 s
f(0.3) =
5.Hard
ReIm−1−2−3−4−5−6−7−812

A system is described by the differential equation y″ + 2y′ + 5y = 2u′ + 14u, 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 = 0.75 s. Find g(0.75).

y″ + 2y′ + 5y = 2u′ + 14ut = 0.75 s
g(0.75) =
6.Hard
t (s)y(t)t = 0.2y(0.2) = ?

Solve y″ + 5y′ + 6y = 0 with y(0) = 6 and y′(0) = −4 using the Laplace transform, and find y(0.2).

y″ + 5y′ + 6y = 0y(0) = 6y′(0) = −4t = 0.2 s
y(0.2) =

Answer key

  1. 1. f(0.3) = −5.187
  2. 2. f′(0⁺) = −21
  3. 3. f(0.4) = 4.424
  4. 4. f(0.3) = 6.476
  5. 5. g(0.75) = 2.894
  6. 6. y(0.2) = 4.994

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