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 first-order system G(s) = 10/(0.8s + 1) receives a step input of size 5 at t = 0, starting from rest. How long does the output take to reach 98 % of its final value? Find t.

G(s) = 10/(0.8s + 1)U = 598 %

t = s

2.Easy

An uncharged capacitor C = 47 µF is charged from a 9 V step source through a resistor R = 22 kΩ. Find the 10–90 % rise time t_r of the capacitor voltage, in ms.

R = 22 kΩC = 47 µFV = 9 V

t_r = ms

3.Medium

A system has the transfer function G(s) = 91/(s² + 11s + 91) and receives a unit step input. Find the damping ratio ζ.

G(s) = 91/(s² + 11s + 91)

ζ =

4.Medium

A system has the transfer function G(s) = 10/(s² + 3s + 5) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 10/(s² + 3s + 5)

σ =

5.Hard

A series RLC circuit with R = 179 Ω, L = 50 mH and C = 1 µF is connected to a 10 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the peak capacitor voltage v_C,max.

R = 179 ΩL = 50 mHC = 1 µFV = 10 V

v_C,max = V

6.Hard

A series RLC circuit with R = 100 Ω, L = 20 mH and C = 2 µF is connected to a 24 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the percent overshoot %OS of the capacitor voltage.

R = 100 ΩL = 20 mHC = 2 µFV = 24 V

%OS = %

Answer key

1. t = 3.13 s
2. t_r = 2272 ms
3. ζ = 0.5766
4. σ = −1.5
5. v_C,max = 12.54 V
6. %OS = 16.3 %

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