Distance Traveled by Harmonic Oscillator in 1 Period

In summary, a harmonic oscillator with an amplitude A travels a distance of 4A in one period of oscillation. The equation for calculating this distance is 2A, but in this specific problem, the answer is 4A. This is because a harmonic oscillator has two degrees of freedom, position and momentum, and the state of the oscillator is uniquely determined by these two variables. Therefore, only when both position and momentum are the same as a previous moment can it be considered one full period.
  • #1
Aoiumi
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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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  • #2
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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  • #3
I think I understand...
 
Last edited:

What is a harmonic oscillator?

A harmonic oscillator is a system that exhibits periodic motion, meaning it repeats the same pattern over and over again. It is characterized by a restoring force that is directly proportional to the displacement from its equilibrium position.

What is the distance traveled by a harmonic oscillator in 1 period?

The distance traveled by a harmonic oscillator in 1 period is equal to the amplitude of the oscillation multiplied by 2π. This is known as the wavelength and represents the total distance traveled by the oscillator from one point to the same point in the next period.

What factors affect the distance traveled by a harmonic oscillator in 1 period?

The distance traveled by a harmonic oscillator in 1 period is affected by three main factors: the amplitude of the oscillation, the frequency of the oscillation, and the mass of the oscillator. A larger amplitude or frequency will result in a longer distance traveled, while a larger mass will result in a shorter distance traveled.

How do you calculate the distance traveled by a harmonic oscillator in 1 period?

The distance traveled by a harmonic oscillator in 1 period can be calculated using the formula: distance = amplitude x 2π. This formula assumes that the oscillator starts and ends at the same point in its motion.

What are some real-life examples of objects that exhibit harmonic motion?

Some examples of objects that exhibit harmonic motion include a swinging pendulum, a mass-spring system, and a guitar string. Other examples include a child on a swing, a bouncing ball, and a tuning fork.

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