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.

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1.Easy

An uncharged capacitor C = 4.7 µF is charged from a 12 V step source through a resistor R = 2.2 kΩ. Find the 10–90 % rise time t_r of the capacitor voltage, in ms.

R = 2.2 kΩC = 4.7 µFV = 12 V

t_r = ms

2.Easy

A first-order system G(s) = 2/(s + 1) receives a step input of size 20 at t = 0, starting from rest. How long does the output take to reach 75 % of its final value? Find t.

G(s) = 2/(s + 1)U = 2075 %

t = s

3.Medium

A system has the transfer function G(s) = 64/(s² + 7s + 32) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 64/(s² + 7s + 32)

t_s = s

4.Medium

A system has the transfer function G(s) = 20/(s² + 9s + 40) and receives a unit step input. Find the peak time t_p of the step response.

G(s) = 20/(s² + 9s + 40)

t_p = s

5.Hard

A mass m = 4 kg hangs on a spring k = 800 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 percent overshoot %OS of the displacement.

m = 4 kgk = 800 N/mc = 45 N·s/mF = 25 N

%OS = %

6.Hard

A mass m = 4 kg hangs on a spring k = 400 N/m with a viscous damper c = 32 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 5 N is suddenly applied. Find the damping ratio ζ.

m = 4 kgk = 400 N/mc = 32 N·s/mF = 5 N

ζ =

Answer key

1. t_r = 22.72 ms
2. t = 1.386 s
3. t_s = 1.143 s
4. t_p = 0.7069 s
5. %OS = 25.62 %
6. ζ = 0.4

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