Relationship between harmonic and circular motions

[Calpalned]

Homework Statement

How is $\frac{v}{v_M} = \frac{\sqrt{A^2 - x^2 }}{A}$ derived?

Homework Equations

n/a

The Attempt at a Solution

I don't see a right angle in the picture anywhere, so I don't see how pythagorean's theorem is valid.

 

[SammyS]

I see three.

What do v and v_m represent?

 

[Calpalned]

I see three.

View attachment 82346

What do v and v_m represent?

Ok, I see where $\sqrt{A^2-x^2}$ came from. However, why are $v_m = A$ and $v=\sqrt{A^2-x^2}$? According to the picture, shouldn't $v=x$?

 

[Calpalned]

Why did the textbook choose to do $\frac{v}{v_M}$?

 

[SammyS]

Why did the textbook choose to do $\frac{v}{v_M}$?

What is it that v and v_m represent? What is the context of this figure and the quantities shown in it ?