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 10 V step source through a resistor R = 10 kΩ. Find the capacitor voltage v_C at t = 5 ms.

R = 10 kΩC = 1 µFV = 10 Vt = 5 ms

v_C = V

2.Easy

An uncharged capacitor C = 10 µF is charged from a 9 V step source through a resistor R = 4.7 kΩ. How long after closing the switch does the capacitor voltage reach 75 % of its final value? Find t in ms.

R = 4.7 kΩC = 10 µFV = 9 V75 %

t = ms

3.Medium

A system has the transfer function G(s) = 89/(s² + 14s + 89) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 89/(s² + 14s + 89)

t_s = s

4.Medium

A system has the transfer function G(s) = 111/(s² + 2s + 37) and receives a unit step input. Find the peak time t_p of the step response.

G(s) = 111/(s² + 2s + 37)

t_p = s

5.Hard

A series RLC circuit with R = 379 Ω, L = 100 mH and C = 1 µF is connected to a 10 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 = 379 ΩL = 100 mHC = 1 µFV = 10 V

ω_n = rad/s

6.Hard

A unity negative feedback loop has G(s) = K/(s(s + 16)). Find the gain K that gives a step response with 30 % overshoot.

G(s) = K/(s(s + 16))%OS = 30 %

K =

Answer key

1. v_C = 3.935 V
2. t = 65.16 ms
3. t_s = 0.5714 s
4. t_p = 0.5236 s
5. ω_n = 3162 rad/s
6. K = 499.8

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