What Differentiates Simple Harmonic Motion from ψ = Amod(t) cos (wavt)?

[whitehorsey]

1. What is the difference between ψ = A_mod(t) cos (w_avt)and the simple harmonic oscillator?

3. A. The amplitude is time dependent
B. The amplitude,A_mod , is twice the amplitude of the simple harmonic oscillator, A.
C. The oscillatory behavior is a function of ? instead of the period, T.

I'm not sure what the difference is. I thought that the equations are similar but that was incorrect.

 

[BvU]

What is ψ for a simple harmonic oscillator ?

 

[whitehorsey]

Simple harmonic oscillator:
ψ = 2A[cos(w_avt) cos(1/2 w_beatt)]

A_mod (t) = 2Acos(1/2 w_beatt)

In the book, it says the maximum amplitude A_mod of the wave changes with time. Would that mean it is A?

 

[BvU]

My simple harmonic oscillator $\ddot x + \omega^2 x = 0$ doesn't have a beat frequency. Only $A\cos(\omega t + \phi)$ with $A$ and $\phi$ constant.