Modeling Periodic Behaviour - Lourdes Mathematics



Hmwk: pg 352 # 1 - 9, 11*

Modeling Periodic Behaviour

Periodic behaviour describes a function that repeats.

Some examples of periodic behaviour are:

1. The outside temperature as a function of time in years.

2. The amount of daylight on a daily basis.

3. The air pressure outside the eardrum as a pure tone is being heard.

4. The electric activity around the heart as viewed on an electrocardiogram (ECG).

5. The population of tent caterpillars; cycle of about 10 years.

6. The voltage on an AC (alternating current) electric circuit.

7. Financial stability in the market; recessions occur about once every 10 years; 1981, 1991, 2001, 2009

8. The motion of the Tacoma’s Bridge before it’s collapse in 1940.

[pic]

Periodic events are characterized by the following descriptors:

• Cycle – one repetition in a repeating process.

• Period (T) – The change in the independent variable (typically time in seconds) corresponding to one cycle.

• Frequency (f) – the number of cycles that occur per every unit of the independent variable. If the independent variable is time measured in seconds then the frequency is measured in s-1 or Hz (Hertz).

• Amplitude – Half the range on a graph.

Ex; If the maximum temperature in Guelph is 28oC and the minimum temperature is –12oC over the seasons then the amplitude is

(28 – (-12))/2 = 20oC

Period and frequency are related by the equations:

[pic] or [pic]

Periodic Behaviour and their Graphs

Determine if each graph describes periodic behaviour. If the graph is periodic then label one cycle, determine the amplitude, period and frequency.

a) Amount of Daylight in Balmaceda, Chile

b) A Normal ECG

[pic]

[pic]

c) Radius of Atoms

[pic]

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Amplitude =

Period =

Frequency =

Amplitude =

Period =

Frequency =

Eqn of the Axis:

Amplitude =

Period =

Frequency =

Eqn of the Axis:

[pic]

Amplitude =

Period =

Frequency =

Eqn of the Axis:

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