Distance Traveled by Harmonic Oscillator in 1 Period

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SUMMARY

The distance traveled by a harmonic oscillator in one complete period of oscillation is definitively 4A, where A represents the amplitude. This conclusion arises from the understanding that the oscillator moves from its maximum positive displacement to its maximum negative displacement and back, covering a total distance of 4A. The discussion clarifies that while the oscillator passes through any given position twice during one period, the unique states of momentum and position define the completion of one oscillation cycle.

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  • Understanding of harmonic oscillators and their properties
  • Familiarity with concepts of amplitude and period
  • Basic knowledge of position and momentum in physics
  • Ability to interpret oscillatory motion graphs
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  • Study the equations of motion for harmonic oscillators
  • Explore the concept of energy conservation in oscillatory systems
  • Learn about phase space and its application to harmonic motion
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Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts related to harmonic oscillators.

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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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