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