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
t (s)y(t)y(∞) = ?

A first-order system G(s) = 10/(s + 20) receives a step input of size 20 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 10/(s + 20)U = 20
y(∞) =
2.Easy
t (s)y(t)10t = ?80 %

A first-order system G(s) = 10/(0.2s + 1) receives a step input of size 1 at t = 0, starting from rest. How long does the output take to reach 80 % of its final value? Find t.

G(s) = 10/(0.2s + 1)U = 180 %
t = s
3.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 88/(s² + 4s + 88) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 88/(s² + 4s + 88)
tp = s
4.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 3/(s² + s + 6) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 3/(s² + s + 6)
tp = s
5.Hard
R(s)+Ks(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 4)). Find the gain K that gives a step response with 15 % overshoot.

G(s) = K/(s(s + 4))%OS = 15 %
K =
6.Hard
+−12 VR = 134 ΩL = 50 mHC = 1 µFvC​

A series RLC circuit with R = 134 Ω, L = 50 mH and C = 1 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 ωn in rad/s.

R = 134 ΩL = 50 mHC = 1 µFV = 12 V
ωn = rad/s

Answer key

  1. 1. y(∞) = 10
  2. 2. t = 0.3219 s
  3. 3. tp = 0.3428 s
  4. 4. tp = 1.31 s
  5. 5. K = 14.97
  6. 6. ωn = 4472 rad/s

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