This applet shows that the Projection of UCM on any diameter of a circle is an example of Linear SHM

The points [math]P_x[/math] and [math]P_y[/math] are projections of the point [i]P[/i] in the [i]x[/i] and [i]y[/i] directions respectively. Those points move with simple harmonic motion. The acceleration equations for those points are also displayed.[br][list][br][*] Control the angular frequency / speed with values of [math]\omega[/math].[br][*] Position vector of the particle and unit vectors showing the direction of velocity and acceleration can be toggled.[br][*] The phase angle can be adjusted (in radians or use degrees with the alt-O keys....so 45 alt-O for [math]45^{\circ}[/math]).[br][/list]