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 = 1 µF is charged from a 5 V step source through a resistor R = 4.7 kΩ. Find the capacitor voltage v_C at t = 9.4 ms.

R = 4.7 kΩC = 1 µFV = 5 Vt = 9.4 ms

v_C = V

2.Easy

An uncharged capacitor C = 47 µF is charged from a 24 V step source through a resistor R = 22 kΩ. Find the capacitor voltage v_C at t = 1034 ms.

R = 22 kΩC = 47 µFV = 24 Vt = 1034 ms

v_C = V

3.Medium

A system has the transfer function G(s) = 33/(s² + s + 11) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 33/(s² + s + 11)

σ =

4.Medium

A system has the transfer function G(s) = 54/(s² + 5s + 54) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 54/(s² + 5s + 54)

%OS = %

5.Hard

A unity negative feedback loop has G(s) = 85/(s(s + 10)). Find the 2 % settling time t_s of the closed-loop step response, using t_s ≈ 4/(ζωₙ).

G(s) = 85/(s(s + 10))

t_s = s

6.Hard

A mass m = 2 kg hangs on a spring k = 800 N/m with a viscous damper c = 12 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 = 2 kgk = 800 N/mc = 12 N·s/mF = 10 N

%OS = %

Answer key

1. v_C = 4.323 V
2. v_C = 15.17 V
3. σ = −0.5
4. %OS = 32.09 %
5. t_s = 0.8 s
6. %OS = 62.09 %

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