MAE 4182 · Lecture 06

Time-Response of First-Order Systems
Course calendar

1 / 9 · Course notes · pp. 1, 3

Time-Domain Analysis

Evaluate the output response in the time domain due to selected input signals.

PASCO How Do I? · Temperature measurements · about 2 min

Can a thermometer be accurate but slow?

Watch for: The measured temperature changes gradually after the sensor's surroundings change.

Watch on YouTube ↗Original source ↗If the player is blocked, use YouTube.

Discuss with your neighbor: If the surroundings change suddenly, must the sensor reading jump instantly too?

This is the sensor's response, not the temperature of an entire room or cup. A first-order approximation assumes reasonably constant surroundings and heat-transfer conditions. Compare changes from the initial temperature, not absolute Celsius, with our unit response.

Impulse

u(t) = δ(t)

0tUnit area

A very brief input with unit area.

Step

u(t) = uₛ(t)

0t1

Switch to one and hold it there.

Ramp

u(t) = t, for t ≥ 0

0t

Increase at a constant rate.

We will calculate the impulse response and the step response.

These drawings show inputs. Signals start at t = 0; the impulse arrow represents unit area, not a finite peak height.

Teaching notes

Begin a new topic after the drone discussion. Time-domain analysis means finding the output as a function of time for a selected input. Name impulse, step, and ramp. The notes calculate only impulse and step responses; do not introduce a ramp-response derivation.

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