# Graph of the Harmonic Oscillation y=Asin(omega x+alpha)

Trigonometric functions are used to describe oscillatory processes (for example, oscillation of pendulum). One of the most important formulas that describes such processes is y=Asin(omega x+alpha), which is called formula of harmonic (or sinusoidal) oscillations. A is called amplitude of oscillation. omega is called frequency of oscillation. The bigger omega the more oscillations per unit of time. alpha is called starting phase of oscillation.

Example. Draw graph of the function y=2sin(x/3-pi/6).

Let's first rewrite function as y=2sin(1/3(x-pi/2)).

Now we can obtain required graph from the graph of the function y=sin(x) in following four steps:

1. Draw graph of the function y=sin(x).
2. Move obtained graph pi/2 units to the right.
3. Compress obtained graph to y-axis with coeffcient 1/3 (actually this means to stretch graph from y-axis with coefficient 3).
4. Stretch obtained graph from x-axis with coefficient 2.

Obtained graph is graph of the function y=2sin(x/3-pi/6) (see figure).