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Physics II forgotten equation (oscillations)

  • Thread starter PCSL
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  • #1
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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 [itex]v=w{\sqrt{A^2x^2}}[/itex] comes from? Thank you.
 
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  • #2
vela
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That equation can't be correct. The units on the RHS work out to be length2/time.
 
  • #3
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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:

[itex]\frac{1}{2}mv_x^2 + \frac{1}{2}kx^2=\frac{1}{2}kA^2[/itex]

[itex]mv_x^2 + kx^2=kA^2[/itex]
 
  • #4
vela
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Try solving for the velocity.
 
  • #5
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Try solving for the velocity.
You get [itex]v={\sqrt{{\frac{k}{m}}A^2x^2}}[/itex] which is equivolaent to [itex]v=w{\sqrt{A^2x^2}}[/itex].
 
  • #6
vela
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No, you don't. How'd you get that?
 
  • #7
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No, you don't. How'd you get that?
[itex]mv_x^2 + kx^2=kA^2[/itex]

Sorry, I'm not gonna 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.
 
  • #8
vela
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Yup, that's the equation I think you were looking for.
 

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