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 5 V step source through a resistor R = 22 kΩ. How long after closing the switch does the capacitor voltage reach 80 % of its final value? Find t in ms.

R = 22 kΩC = 1 µFV = 5 V80 %

t = ms

2.Easy

A first-order system G(s) = 50/(s + 10) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 50/(s + 10)U = 5

y(∞) =

3.Medium

A system has the transfer function G(s) = 255/(s² + 3s + 85) and receives a unit step input. Find the peak time t_p of the step response.

G(s) = 255/(s² + 3s + 85)

t_p = s

4.Medium

A system has the transfer function G(s) = 42/(s² + 14s + 84) and receives a unit step input. Find the peak time t_p of the step response.

G(s) = 42/(s² + 14s + 84)

t_p = s

5.Hard

A series RLC circuit with R = 65 Ω, L = 500 mH and C = 4.7 µF is connected to a 10 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 = 65 ΩL = 500 mHC = 4.7 µFV = 10 V

%OS = %

6.Hard

A series RLC circuit with R = 120 Ω, L = 20 mH and C = 2 µF is connected to a 12 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 = 120 ΩL = 20 mHC = 2 µFV = 12 V

%OS = %

Answer key

1. t = 35.41 ms
2. y(∞) = 25
3. t_p = 0.3454 s
4. t_p = 0.531 s
5. %OS = 73.01 %
6. %OS = 9.478 %

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