## Simple harmonic functions

A function  is called a simple harmonic function (or, harmonic oscillation) if

 or (1-1)

with .

(S)

(C)

Amplitude, period, and phase. The absolute value  of  represents the largest value (in absolute value) attained by the function , and is called the amplitude of . The interval  represents one cycle (or, one complete oscillation), and is called period of . Note that if then is a periodic function with period  . is called the phase shift (or, the initial phase) of .

Graph. Each cycle repeats itself for every interval

for .

The graph of one cycle is given by the simple harmonic function (1-1) with phase shift .

Department of Mathematics