Simple Harmonic Motion:Geometrical Solutions of Equations of Motions

Conventionally while we talk about geometry associated with a simple harmonic oscillator, we draw a circle with a radius equal to the amplitude of Oscillator and imagine a particle moving along the perimeter with a frequency same as that of Oscillator and then the x coordinate of the position of the particle gives the value of the displacement of the Oscillator. Here we discuss another kind of diagram (polar plot) depicting dynamics of Oscillator and come up with a solution to boundary and initial value problem geometrically.