Harmonic Oscillation: Proving Distance = 4A

[nns91]

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 ?

 

[LowlyPion]

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?

 

[nns91]

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

 

[LowlyPion]

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.