Periodic Motion Introduction
From MyMCAT
Introduction
Any object which moves periodically in some manner is said to be undergoing periodic motion. Periodic motion can be observed in one dimension, as in the case of a weight hanging by a spring bouncing up and down, or in two dimensions, as in the case of a pendulum swinging.
Amplitude
The amplitude of a object in periodic motion refers to the maximum amount of displacement in the medium from its rest position. In a sense, the amplitude is the distance from "rest to crest."
In the case of a box hanging from a spring, the amplitude would be measured from either how far up or down it reaches to the equilibrium position (where the box would be if it weren't moving).
In the case of objects undergoing circular motion (two dimensions), the amplitude is simply the radius of the circle. (If one observed the displacement of the object with respect to just one dimension it would look just like the spring going up and down, or left and right depending on which view you take...)
Period and Frequency
The period, T of the object is the time it takes to complete one cycle. (The time it takes to move from a position and then return back to that exact same position.) T is measured in seconds, s, and intuitively a larger T implies a slower period but it does not imply a smaller or larger velocity.
The frequency, ƒ, of the object is the number of cycles completed per second. ƒ is measured in 1/seconds, or s-1, or simply Hertz, Hz.
Period and frequency are in fact related to each other by the following equation
A larger period, implies a shorter frequency, and vice versa.
