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

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

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

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.

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!

Pythagoras famously quoted:

Do not say a little in many words but a great deal in a few

And his theorem is a draconian illustration of these words.

* This happens to be one of my favorite proofs of the theorem, but feel free to explore the legion others that are in existence, like this one :

Good Day!

Hyperboloid.

//ControlledChaos\

Demoralise.