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

An uncharged capacitor C = 1 µF is charged from a 10 V step source through a resistor R = 10 kΩ. Find the 10–90 % rise time t_r of the capacitor voltage, in ms.

R = 10 kΩC = 1 µFV = 10 V

t_r = ms

2.Easy

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 2. At t = 1 s it reads 1.4. Find the time constant τ.

y(∞) = 2y(1) = 1.4

τ = s

3.Medium

A system has the transfer function G(s) = 200/(s² + 8s + 100) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 200/(s² + 8s + 100)

t_s = s

4.Medium

A system has the transfer function G(s) = 186/(s² + 3s + 93) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 186/(s² + 3s + 93)

t_s = s

5.Hard

A unity negative feedback loop has G(s) = 30/(s(s + 5)). Find the 2 % settling time t_s of the closed-loop step response, using t_s ≈ 4/(ζωₙ).

G(s) = 30/(s(s + 5))

t_s = s

6.Hard

A mass m = 5 kg hangs on a spring k = 400 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 = 10 N is suddenly applied. Find the percent overshoot %OS of the displacement.

m = 5 kgk = 400 N/mc = 45 N·s/mF = 10 N

%OS = %

Answer key

1. t_r = 21.97 ms
2. τ = 0.8306 s
3. t_s = 1 s
4. t_s = 2.667 s
5. t_s = 1.6 s
6. %OS = 16.06 %

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