Uncovering the History of SHM: From Newton to Trig Functions

[Crosson]

I am wondering if anyone knows the history of the mathematical study of simple harmonic motion. Who first set up the equation:

$$\frac{d^2X(t)}{dt^2} +\frac{k}{m} X(t) = 0$$

Was it Newton? Hooke? Did they know about uniqueness of solutions?

The trig functions occupy such a cetral role these days in the study of calculus, this differential equation has a magic trick feeling to it. If the discoverer's of this equation viewed it in a similar context as ourselves, it must have been one of the most instantly satisfying confirmations of Newton's Mechanics.

 

[arildno]

Interesting question!
You can certainly disregard Hooke, and also, I think, Newton&Leibniz.
If I were to make a bet, I'd say one of the Bernoullis or Euler.

However, since Hooke's law was known to Newton, it might well be that Newton was aware of this. If he ever published anything to that effect, is another matter.

(However, I'm not speaking from knowledge here; just speculating..)

 

[krab]

Atwood, I think