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 = 22 µF is charged from a 5 V step source through a resistor R = 4.7 kΩ. Find the capacitor voltage v_C at t = 103.4 ms.

R = 4.7 kΩC = 22 µFV = 5 Vt = 103.4 ms

v_C = V

2.Easy

An uncharged capacitor C = 10 µF is charged from a 12 V step source through a resistor R = 100 kΩ. Find the 10–90 % rise time t_r of the capacitor voltage, in ms.

R = 100 kΩC = 10 µFV = 12 V

t_r = ms

3.Medium

A system has the transfer function G(s) = 144/(s² + 3s + 48) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 144/(s² + 3s + 48)

t_s = s

4.Medium

A system has the transfer function G(s) = 52/(s² + 2s + 52) and receives a unit step input. Find the damping ratio ζ.

G(s) = 52/(s² + 2s + 52)

ζ =

5.Hard

A series RLC circuit with R = 19 Ω, L = 10 mH and C = 10 µF is connected to a 24 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the time t_p of the first voltage peak, in ms.

R = 19 ΩL = 10 mHC = 10 µFV = 24 V

t_p = ms

6.Hard

A series RLC circuit with R = 32 Ω, L = 100 mH and C = 100 µF is connected to a 24 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 = 32 ΩL = 100 mHC = 100 µFV = 24 V

ω_n = rad/s

Answer key

1. v_C = 3.161 V
2. t_r = 2197 ms
3. t_s = 2.667 s
4. ζ = 0.1387
5. t_p = 1.042 ms
6. ω_n = 316.2 rad/s

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