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 = 47 µF is charged from a 10 V step source through a resistor R = 4.7 kΩ. Find the capacitor voltage v_C at t = 110.5 ms.

R = 4.7 kΩC = 47 µFV = 10 Vt = 110.5 ms

v_C = V

2.Easy

A first-order system G(s) = 1/(s + 2) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 1/(s + 2)U = 5

y(∞) =

3.Medium

A system has the transfer function G(s) = 19/(s² + 7s + 19) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 19/(s² + 7s + 19)

t_s = s

4.Medium

A system has the transfer function G(s) = 279/(s² + 3s + 93) and receives a unit step input. Find the peak time t_p of the step response.

G(s) = 279/(s² + 3s + 93)

t_p = s

5.Hard

A mass m = 0.5 kg hangs on a spring k = 200 N/m with a viscous damper c = 3 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 50 N is suddenly applied. Find the percent overshoot %OS of the displacement.

m = 0.5 kgk = 200 N/mc = 3 N·s/mF = 50 N

%OS = %

6.Hard

A series RLC circuit with R = 391 Ω, L = 500 mH and C = 4.7 µF is connected to a 12 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 = 391 ΩL = 500 mHC = 4.7 µFV = 12 V

ω_n = rad/s

Answer key

1. v_C = 3.935 V
2. y(∞) = 2.5
3. t_s = 1.143 s
4. t_p = 0.3298 s
5. %OS = 62.09 %
6. ω_n = 652.3 rad/s

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