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
+−10 VR = 4.7 kΩC = 22 µFvC​

An uncharged capacitor C = 22 µF is charged from a 10 V step source through a resistor R = 4.7 kΩ. Find the capacitor voltage vC at t = 310.2 ms.

R = 4.7 kΩC = 22 µFV = 10 Vt = 310.2 ms
vC = V
2.Easy
t (s)y(t)101 s9

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 10. At t = 1 s it reads 9. Find the time constant τ.

y(∞) = 10y(1) = 9
τ = s
3.Medium
t (s)y(t)1

A system has the transfer function G(s) = 95/(s² + 5s + 95) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 95/(s² + 5s + 95)
σ =
4.Medium
t (s)y(t)3

A system has the transfer function G(s) = 141/(s² + 8s + 47) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 141/(s² + 8s + 47)
ωn = rad/s
5.Hard
t (s)y(t)1tp​ = 0.2 s40 %

The step response of a second-order system without zeros shows 40 % overshoot, and the first peak occurs at t = 0.2 s. Find the natural frequency ωn.

%OS = 40 %tp = 0.2 s
ωn = rad/s
6.Hard
R(s)+145s(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = 145/(s(s + 6)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 145/(s(s + 6))
ts = s

Answer key

  1. 1. vC = 9.502 V
  2. 2. τ = 0.4343 s
  3. 3. σ = −2.5
  4. 4. ωn = 6.856 rad/s
  5. 5. ωn = 16.36 rad/s
  6. 6. ts = 1.333 s

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