Harmonic Oscillation: Proving Distance = 4A

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Homework Help Overview

The problem involves a scenario where a man oscillates back and forth due to superelastic suspenders, with an amplitude denoted as A. The discussion centers on determining the total distance traveled in one complete period of oscillation and the displacement over that period.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between distance and displacement, noting that displacement is zero after one complete oscillation. There is an assertion that the total distance traveled is 4A, but participants seek clarification on how to substantiate this claim. Questions arise regarding the displacement at specific intervals, particularly at π/2.

Discussion Status

The conversation is ongoing, with participants exploring different interpretations of the problem. Some have provided insights into the movement at various intervals, while others are questioning the definitions and relationships involved in the oscillation. There is no explicit consensus yet.

Contextual Notes

Participants are working within the constraints of the problem as posed, focusing on the definitions of distance and displacement in the context of harmonic motion. There is mention of potential confusion regarding notation and terminology.

nns91
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Homework Statement



1. A man's superelastic suspenders catch on a fence post, he flies back and forth, oscillating with an amplitude A. What distance does he movee in one period ? What is his displacement over 1 period

Homework Equations



x=Acos(wt)

The Attempt at a Solution



I know that the displacement is 0 since he returns to the original position. I also know that the distance should be 4A but I don't know how to explain it. It just makes sense to me.

How do I prove that distance is 4A ?
 
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nns91 said:

Homework Statement



1. A man's superelastic suspenders catch on a fence post, he flies back and forth, oscillating with an amplitude A. What distance does he movee in one period ? What is his displacement over 1 period

Homework Equations



x=Acos(wt)

The Attempt at a Solution



I know that the displacement is 0 since he returns to the original position. I also know that the distance should be 4A but I don't know how to explain it. It just makes sense to me.

How do I prove that distance is 4A ?

What is the displacement for π/2 and each subsequent π/2 interval? How many π/2 intervals in a revolution?
 
What do you mean by n ?

If you mean n/2 by the angle then it will move A for each n/2 and there are 4n/2 so it moves 4A
 
nns91 said:
What do you mean by n ?

If you mean n/2 by the angle then it will move A for each n/2 and there are 4n/2 so it moves 4A

The font doesn't show it clearly but π is pi.

The font doesn't show it clearly but π is pi.
 

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