Take a little ball that is going round and round,
Take its x-shadow and it will be found

That x equals A cosine omega t.
Differentiate twice and it's clear to see

That the ratio of a to x right there
Is a negative constant, omega squared.

Now a mass on a spring gets a Hooke's law force
And obeys the equation of motion, of course.

So a over x is minus k over m.
There's that negative constant again!

Pull the mass aside and then let it go,
Setting it oscillating to-and-fro

And its motion is simple harmonic, I say.
That's why we study it. Have a nice day!