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

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 18. Find the time constant τ.

y(∞) = 20y(1) = 18

τ = s

2.Easy

An uncharged capacitor C = 22 µF is charged from a 5 V step source through a resistor R = 100 kΩ. How long after closing the switch does the capacitor voltage reach 50 % of its final value? Find t in ms.

R = 100 kΩC = 22 µFV = 5 V50 %

t = ms

3.Medium

A system has the transfer function G(s) = 17/(s² + 3s + 17) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 17/(s² + 3s + 17)

t_s = s

4.Medium

A system has the transfer function G(s) = 40/(s² + 3s + 20) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 40/(s² + 3s + 20)

t_s = s

5.Hard

A series RLC circuit with R = 253 Ω, L = 100 mH and C = 1 µF is connected to a 24 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the undamped natural frequency ω_n in rad/s.

R = 253 ΩL = 100 mHC = 1 µFV = 24 V

ω_n = rad/s

6.Hard

A unity negative feedback loop has G(s) = K/(s(s + 6)). Find the gain K that gives a step response with 20 % overshoot.

G(s) = K/(s(s + 6))%OS = 20 %

K =

Answer key

1. τ = 0.4343 s
2. t = 1525 ms
3. t_s = 2.667 s
4. t_s = 2.667 s
5. ω_n = 3162 rad/s
6. K = 43.29

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