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 = 2.2 µF is charged from a 10 V step source through a resistor R = 100 kΩ. Find the 10–90 % rise time t_r of the capacitor voltage, in ms.

R = 100 kΩC = 2.2 µFV = 10 V

t_r = ms

2.Easy

An uncharged capacitor C = 1 µF is charged from a 10 V step source through a resistor R = 47 kΩ. Find the 10–90 % rise time t_r of the capacitor voltage, in ms.

R = 47 kΩC = 1 µFV = 10 V

t_r = ms

3.Medium

A system has the transfer function G(s) = 46/(s² + 4s + 92) and receives a unit step input. Find the natural frequency ω_n in rad/s.

G(s) = 46/(s² + 4s + 92)

ω_n = rad/s

4.Medium

A system has the transfer function G(s) = 38/(s² + 6s + 19) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 38/(s² + 6s + 19)

%OS = %

5.Hard

A mass m = 20 kg hangs on a spring k = 500 N/m with a viscous damper c = 20 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 damping ratio ζ.

m = 20 kgk = 500 N/mc = 20 N·s/mF = 100 N

ζ =

6.Hard

A mass m = 2 kg hangs on a spring k = 800 N/m with a viscous damper c = 48 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 damping ratio ζ.

m = 2 kgk = 800 N/mc = 48 N·s/mF = 25 N

ζ =

Answer key

1. t_r = 483.4 ms
2. t_r = 103.3 ms
3. ω_n = 9.592 rad/s
4. %OS = 5.077 %
5. ζ = 0.1
6. ζ = 0.6

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