# Harmonic oscillator derivation

Tags:
1. Sep 19, 2015

I was wondering how to derive the sinusoidal equation for the simple armonic oscillator. But I am currently trying to understand this step in this webpage:

I don't get where do P and Q come from and why it is summing pe^iwt + qe^-iwt. please I need some help. The rest of it pretty much makes sense.

2. Sep 19, 2015

### SteamKing

Staff Emeritus
I'm not sure what an "armonic" oscillator is, unless you mean "harmonic".

The differential equation of the harmonic oscillator is linear and homogeneous, so the general solution is composed of the sum of all the solutions obtained by solving the characteristic equation.

If you've studied ordinary differential equations, this should be obvious. If you haven't, then you should study ODEs a little before proceeding further.

3. Sep 19, 2015