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
+−24 VR = 1 kΩC = 2.2 µFvC​

An uncharged capacitor C = 2.2 µF is charged from a 24 V step source through a resistor R = 1 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 1 kΩC = 2.2 µFV = 24 V
tr = ms
2.Easy
t (s)y(t)43 s3.6

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 4. At t = 3 s it reads 3.6. Find the time constant τ.

y(∞) = 4y(3) = 3.6
τ = s
3.Medium
t (s)y(t)3

A system has the transfer function G(s) = 108/(s² + 7s + 36) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 108/(s² + 7s + 36)
σ =
4.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 104/(s² + 7s + 52) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 104/(s² + 7s + 52)
tp = s
5.Hard
R(s)+55s(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = 55/(s(s + 5)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 55/(s(s + 5))
ts = s
6.Hard
R(s)+65s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 65/(s(s + 8)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 65/(s(s + 8))
ts = s

Answer key

  1. 1. tr = 4.834 ms
  2. 2. τ = 1.303 s
  3. 3. σ = −3.5
  4. 4. tp = 0.4983 s
  5. 5. ts = 1.6 s
  6. 6. ts = 1 s

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