Greenwood press

PERIODIC FUNCTIONS
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Hours of daylight for Minneapolis over a period of two years. Daylight patterns 
throughout a year are predictable in most cities through sinusoidal modeling.
Heart-rate monitors detect electrical
pulses in an EKG to check if the
heart is beating regularly.

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New periodic functions can be created by adding or multiplying two or more
of them. You can see this when you toss two pebbles into a pond. The overlap of
the waves will be a new wave. When audio speakers are arranged in an audito-
rium, they have to be positioned carefully so that the sound waves emerging from
them do not cancel one another out or create a beat that competes with the music.
Fluorescent light bulbs produce a pulsing light that sometimes adds to the cycli-
cal refresh rate on computer screens to produce rapid light bursts that can make
it hard for some people to read the computer display.
Commodity prices often follow a cyclical pattern. Hire rates for temporary-
employment firms appear to form a sine curve. In biology, populations of some
species of animals such as rabbits in a forest will vary over time in a cyclic pat-
tern. When this happens, it is likely that a predator species such as a fox also has
a periodic population pattern that mirrors the rabbit pattern. If there are more
foxes, then there are fewer rabbits; if there are fewer foxes, then there are more
rabbits. In many environments, these periodic relationships continue over time.
The populations of the predator and prey do not level off.
A thermostat is an instrument used to regulate heating and cooling systems,
such as an air conditioner or oven. Once a person sets the thermostat on an oven
for a certain temperature, it will heat up until reaching that temperature, and then
stay close to that temperature until the thermostat is changed. For example, if the
oven is set to 400° Fahrenheit, it will gradually rise to that level for the first
twenty minutes, and then stay at 400° until the temperature is changed or the
oven is turned off. Since temperature naturally slightly varies in the air, it would
also slightly change in the oven, but still oscillate near 400°. This eventual peri-
odic function is shown in below.
The cruise control in an automobile is another device that utilizes periodic
behavior for a function that describes the velocity of an automobile on a highway
as a function of time. As the car accelerates onto the highway, its velocity will
increase and then level off near the speed that is set for the cruise control, usu-
ally the highway’s speed limit. If the road has elevation changes, then the speed
of the automobile in cruise control will vary slightly, since movement on hills
requires different amounts of power on the automobile’s engine. However, sim-
ilar to a thermostat, the slight variability in speed will not affect the long-term
periodic behavior of the graph describing the automobile’s velocity until the
brakes are touched.