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 = 1 kΩC = 1 µFvC​

An uncharged capacitor C = 1 µF is charged from a 12 V step source through a resistor R = 1 kΩ. How long after closing the switch does the capacitor voltage reach 98 % of its final value? Find t in ms.

R = 1 kΩC = 1 µFV = 12 V98 %
t = ms
2.Easy
t (s)y(t)501 s20

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 50. At t = 1 s it reads 20. Find the time constant τ.

y(∞) = 50y(1) = 20
τ = s
3.Medium
t (s)y(t)3

A system has the transfer function G(s) = 39/(s² + 2s + 13) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 39/(s² + 2s + 13)
ωn = rad/s
4.Medium
t (s)y(t)0.5?

A system has the transfer function G(s) = 44/(s² + 10s + 88) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 44/(s² + 10s + 88)
%OS = %
5.Hard
+−5 VR = 30 ΩL = 500 mHC = 22 µFvC​

A series RLC circuit with R = 30 Ω, L = 500 mH and C = 22 µF is connected to a 5 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the undamped natural frequency ωn in rad/s.

R = 30 ΩL = 500 mHC = 22 µFV = 5 V
ωn = rad/s
6.Hard
R(s)+295s(s + 20)G(s)C(s)−

A unity negative feedback loop has G(s) = 295/(s(s + 20)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 295/(s(s + 20))
ts = s

Answer key

  1. 1. t = 3.912 ms
  2. 2. τ = 1.958 s
  3. 3. ωn = 3.606 rad/s
  4. 4. %OS = 13.82 %
  5. 5. ωn = 301.5 rad/s
  6. 6. ts = 0.4 s

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