Distance Traveled by Harmonic Oscillator in 1 Period

AI Thread Summary
A harmonic oscillator with an amplitude A travels a total distance of 4A in one complete period of oscillation. This is because the oscillator moves from the maximum positive amplitude to the maximum negative amplitude and back, covering the distance twice. The discussion highlights the importance of understanding the relationship between position and momentum in determining the state of the oscillator. The initial confusion about the distance traveled was clarified, emphasizing that the total distance accounts for the entire path taken during the oscillation. Understanding these concepts is crucial for solving problems related to harmonic motion.
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Homework Statement


A harmonic oscillator oscillates with an amplitude A. In one period of oscillation, what is the distance traveled by the oscillator?


Homework Equations



I'm not sure which equation applies if any?

The Attempt at a Solution


My guess was 2A but the answer was 4A.

I'm sure this is very easy, but can you please point me in the right direction?
 
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A harmonic oscillator is a system with two degrees of freedom,position and momentum.Any two points within the range of oscillation is passed twice but the state of the oscillator is not the same in the moments that the oscillator is passing that point.In fact the state of the oscillator is uniquely determined by its momentum and position(there maybe other choices too). So only when you reach a point that both position and momentum are the same as a nearly past moment,you can tell one period is finished.
 
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I think I understand...
 
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