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 = 100 µF is charged from a 24 V step source through a resistor R = 22 kΩ. How long after closing the switch does the capacitor voltage reach 98 % of its final value? Find t in ms.

R = 22 kΩC = 100 µFV = 24 V98 %

t = ms

2.Easy

An uncharged capacitor C = 4.7 µF is charged from a 12 V step source through a resistor R = 22 kΩ. Find the capacitor voltage v_C at t = 72.38 ms.

R = 22 kΩC = 4.7 µFV = 12 Vt = 72.38 ms

v_C = V

3.Medium

A system has the transfer function G(s) = 13/(s² + 5s + 13) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 13/(s² + 5s + 13)

t_s = s

4.Medium

A system has the transfer function G(s) = 80/(s² + 7s + 80) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 80/(s² + 7s + 80)

%OS = %

5.Hard

A mass m = 1 kg hangs on a spring k = 1000 N/m with a viscous damper c = 19 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 time t_p at which the displacement is largest.

m = 1 kgk = 1000 N/mc = 19 N·s/mF = 5 N

t_p = s

6.Hard

A unity negative feedback loop has G(s) = 255/(s(s + 6)). Find the 2 % settling time t_s of the closed-loop step response, using t_s ≈ 4/(ζωₙ).

G(s) = 255/(s(s + 6))

t_s = s

Answer key

1. t = 8606 ms
2. v_C = 6.041 V
3. t_s = 1.6 s
4. %OS = 26.29 %
5. t_p = 0.1042 s
6. t_s = 1.333 s

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