## The simple harmonic oscillator

Anonymous asked: Please explain the intuition of solving the SHM equation.

Okay Anon! Here you go, this is my rendition.

## The problem

You have a mass suspended on a spring. We want to know where the mass will be at any instant of time.

Describe the motion of the mass

## The physical solution

Now before we get on to the math, let us first visualize the motion by attaching a spray paint bottle as the mass.

Oh, wait that seems like a function that we are familiar with - The sinusoid.

Without even having to write down a single equation, we have found out the solution to our problem. The motion that is traced by the mass is a sinusoid.

## But what do I mean by a sinusoid ?

If you took the plotted paper and tried to create that function with the help of sum of polynomials i.e x, x^{2}, x^{3} … Now you this what it would like :

By taking an infinite of these polynomial sums you get the function Since this series of polynomial occurs a lot, its given the name - sine.

I hope this shed some light on the intuition of the SHM equation. Have fun!