  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.
