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 = 100 kΩC = 100 µFvC​

An uncharged capacitor C = 100 µF is charged from a 12 V step source through a resistor R = 100 kΩ. How long after closing the switch does the capacitor voltage reach 98 % of its final value? Find t in ms.

R = 100 kΩC = 100 µFV = 12 V98 %
t = ms
2.Easy
t (s)y(t)201 s10

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 20. At t = 1 s it reads 10. Find the time constant τ.

y(∞) = 20y(1) = 10
τ = s
3.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 134/(s² + 5s + 67) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 134/(s² + 5s + 67)
tp = s
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 41/(s² + 7s + 41) and receives a unit step input. Find the damping ratio ζ.

G(s) = 41/(s² + 7s + 41)
ζ =
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 10 % overshoot.

G(s) = K/(s(s + 4))%OS = 10 %
K =
6.Hard
k = 1000 N/mc = 38 N·s/mm = 1 kgF = 20 Nx(t)

A mass m = 1 kg hangs on a spring k = 1000 N/m with a viscous damper c = 38 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 20 N is suddenly applied. Find the largest displacement xmax in mm.

m = 1 kgk = 1000 N/mc = 38 N·s/mF = 20 N
xmax = mm

Answer key

  1. 1. t = 39120 ms
  2. 2. τ = 1.443 s
  3. 3. tp = 0.4031 s
  4. 4. ζ = 0.5466
  5. 5. K = 11.45
  6. 6. xmax = 21.89 mm

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