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
+−9 VR = 22 kΩC = 100 µFvC​

An uncharged capacitor C = 100 µF is charged from a 9 V step source through a resistor R = 22 kΩ. How long after closing the switch does the capacitor voltage reach 75 % of its final value? Find t in ms.

R = 22 kΩC = 100 µFV = 9 V75 %
t = ms
2.Easy
t (s)y(t)510 s3.5

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 5. At t = 10 s it reads 3.5. Find the time constant τ.

y(∞) = 5y(10) = 3.5
τ = s
3.Medium
t (s)y(t)1

A system has the transfer function G(s) = 40/(s² + 7s + 40) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 40/(s² + 7s + 40)
ωn = rad/s
4.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 90/(s² + 11s + 90) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 90/(s² + 11s + 90)
tp = s
5.Hard
R(s)+Ks(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 2)). Find the gain K that gives a step response with 5 % overshoot.

G(s) = K/(s(s + 2))%OS = 5 %
K =
6.Hard
R(s)+Ks(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 6)). Find the gain K that gives a step response with 5 % overshoot.

G(s) = K/(s(s + 6))%OS = 5 %
K =

Answer key

  1. 1. t = 3050 ms
  2. 2. τ = 8.306 s
  3. 3. ωn = 6.325 rad/s
  4. 4. tp = 0.4064 s
  5. 5. K = 2.1
  6. 6. K = 18.9

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