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

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The discussion highlights the key differences between the time-dependent amplitude function ψ = Amod(t) cos(wavt) and the equation for a simple harmonic oscillator. The amplitude in the first equation varies over time, while in the simple harmonic oscillator, it remains constant. Additionally, the amplitude in the time-dependent function is noted to be twice that of the simple harmonic oscillator. The oscillatory behavior in the time-dependent case is influenced by a different variable than the period of the simple harmonic oscillator. Overall, the primary distinction lies in the time-varying nature of the amplitude in the first equation compared to the constant amplitude in the simple harmonic oscillator.
whitehorsey
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1. What is the difference between ψ = Amod(t) cos (wavt)and the simple harmonic oscillator?

3. A. The amplitude is time dependent
B. The amplitude,Amod , 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.
 
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What is ψ for a simple harmonic oscillator ?
 
Simple harmonic oscillator:
ψ = 2A[cos(wavt) cos(1/2 wbeatt)]

Amod (t) = 2Acos(1/2 wbeatt)

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