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
+−12 VR = 47 kΩC = 47 µFvC​

An uncharged capacitor C = 47 µF is charged from a 12 V step source through a resistor R = 47 kΩ. Find the capacitor voltage vC at t = 4418 ms.

R = 47 kΩC = 47 µFV = 12 Vt = 4418 ms
vC = V
2.Easy
t (s)y(t)203 s8

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 20. At t = 3 s it reads 8. Find the time constant τ.

y(∞) = 20y(3) = 8
τ = s
3.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 29/(s² + 6s + 58) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 29/(s² + 6s + 58)
ωn = rad/s
4.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 90/(s² + 3s + 45) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 90/(s² + 3s + 45)
tp = s
5.Hard
R(s)+Ks(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 12)). Find the gain K that gives a step response with 30 % overshoot.

G(s) = K/(s(s + 12))%OS = 30 %
K =
6.Hard
R(s)+Ks(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 12)). Find the gain K that gives a step response with 5 % overshoot.

G(s) = K/(s(s + 12))%OS = 5 %
K =

Answer key

  1. 1. vC = 10.38 V
  2. 2. τ = 5.873 s
  3. 3. ωn = 7.616 rad/s
  4. 4. tp = 0.4805 s
  5. 5. K = 281.1
  6. 6. K = 75.59

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