Physics II forgotten equation (oscillations)

[PCSL]

I am reviewing for a test on oscillations and I have no clue how I derived a formula I used for my homework.

Could anyone help me figure out where the equation v=w{\sqrt{A^2x^2}} comes from? Thank you.

 

[vela]

That equation can't be correct. The units on the RHS work out to be length²/time.

 

[PCSL]

That equation can't be correct. The units on the RHS work out to be length²/time.

I actually just found the equation in the book, it comes from the conservations of energy formula. I don't understand how it can work for the same reason you listed, that's why I am confused. And I'm 100% sure I am copying it down correctly.

It is derived from:

\frac{1}{2}mv_x^2 + \frac{1}{2}kx^2=\frac{1}{2}kA^2

mv_x^2 + kx^2=kA^2

 

[vela]

Try solving for the velocity.

 

[PCSL]

Try solving for the velocity.

You get v={\sqrt{{\frac{k}{m}}A^2x^2}} which is equivolaent to v=w{\sqrt{A^2x^2}}.

 

[vela]

No, you don't. How'd you get that?

 

[PCSL]

No, you don't. How'd you get that?

mv_x^2 + kx^2=kA^2

Sorry, I'm not going to use latex for this so I can do it faster.

mv^2=kA^2-kx^2

v^2=(kA^2-kx^2)/m

v^2= (k/m)(A^2-x^2)

v=sqrt((w^2)(A^2-x^2))

v=w(sqrt(A^2-x^2))

I think that was actually beneficial for me typing that out lol.

 

[vela]

Yup, that's the equation I think you were looking for.