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

An uncharged capacitor C = 1 µF is charged from a 24 V step source through a resistor R = 1 kΩ. Find the capacitor voltage v_C at t = 0.5 ms.

R = 1 kΩC = 1 µFV = 24 Vt = 0.5 ms

v_C = V

2.Easy

A first-order system G(s) = 2.5/(0.8s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 2.5/(0.8s + 1)U = 2

y(∞) =

3.Medium

A system has the transfer function G(s) = 51/(s² + 3s + 51) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 51/(s² + 3s + 51)

t_s = s

4.Medium

A system has the transfer function G(s) = 50/(s² + 11s + 100) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 50/(s² + 11s + 100)

σ =

5.Hard

A mass m = 20 kg hangs on a spring k = 2000 N/m with a viscous damper c = 120 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 100 N is suddenly applied. Find the percent overshoot %OS of the displacement.

m = 20 kgk = 2000 N/mc = 120 N·s/mF = 100 N

%OS = %

6.Hard

A mass m = 20 kg hangs on a spring k = 200 N/m with a viscous damper c = 13 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 25 N is suddenly applied. Find the largest displacement x_max in mm.

m = 20 kgk = 200 N/mc = 13 N·s/mF = 25 N

x_max = mm

Answer key

1. v_C = 9.443 V
2. y(∞) = 5
3. t_s = 2.667 s
4. σ = −5.5
5. %OS = 37.23 %
6. x_max = 215.4 mm

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