Step response worksheet with answers

Free printable Step response worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

A first-order system G(s) = 20/(s + 20) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 20/(s + 20)U = 5

y(∞) =

2.Easy

A first-order system G(s) = 5/(0.2s + 1) receives a step input of size 1 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 5/(0.2s + 1)U = 1

y(∞) =

3.Medium

A system has the transfer function G(s) = 26/(s² + 8s + 52) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 26/(s² + 8s + 52)

σ =

4.Medium

A system has the transfer function G(s) = 49/(s² + 16s + 98) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 49/(s² + 16s + 98)

σ =

5.Hard

A series RLC circuit with R = 181 Ω, L = 500 mH and C = 22 µF is connected to a 12 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the undamped natural frequency ω_n in rad/s.

R = 181 ΩL = 500 mHC = 22 µFV = 12 V

ω_n = rad/s

6.Hard

A mass m = 20 kg hangs on a spring k = 100 N/m with a viscous damper c = 45 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 25 N is suddenly applied. Find the time t_p at which the displacement is largest.

m = 20 kgk = 100 N/mc = 45 N·s/mF = 25 N

t_p = s

Answer key

1. y(∞) = 5
2. y(∞) = 5
3. σ = −4
4. σ = −8
5. ω_n = 301.5 rad/s
6. t_p = 1.626 s

Full step-by-step solutions: practise this topic on examproblems.com.