Question

As a person travels on a Ferris wheel their height above the ground rises and falls. If you plot the height of the person above the ground on a graph, the graph will rise and fall, similar to the graph of sine or cosine. What is another situation where a real world setting models the periodic graph of sine or cosine?

Answer 1

Let's think about a classic example:

Simple harmonic motion is periodic back and forth motion, in which a body oscillates from one side of its equilibrium position to the other, in a given direction, and in equal intervals of time. For example, it is the case of a body hanging from a spring oscillating up and down. The object oscillates about the equilibrium position when it is separated from it and released. In this case the body goes up and down.

The position of the object as a function of the time can be described as follows:

`x(t)=Acos(\omega t+\phi)`

Where:

A = amplitude of the movement

x = elongation or displacement with respect to the equilibrium point.

ω = Angular frequency

Φ = Initial phase

t = time