Determine an expression for the period of motion.

In summary, the conversation involved solving a problem related to gravity using the equation F = -4Gπρm/3r^, with r^ as a unit vector. The solution involved comparing this equation to the standard simple harmonic motion equation, F = -kx, and determining the equivalent for k in the gravity equation. This was found to be k = 4Gπρm/3. The conversation then moved on to finding the period of motion, which was solved by expressing it in terms of the frequency ω, and then substituting the value for ω in terms of k and m. Finally, the solution was simplified to t = 2π/√(4Gπρm/3)/
  • #36
The mass should cancel and thus not appear in your final version.
 
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  • #37
What I meant by saying the equation was wrong was in your #3 post you put the equation wrong. In actual fact the mass should come after the division. Thus

gif.latex?F%20=%20\frac{4G\pi%20\rho%20}{3}%20m%20r%20\hat{r}.gif


and not

gif.latex?F%20=%20\frac{4G\pi%20\rho%20m}{3}%20r.gif


which would make k = 4Gπρ and not k = 4Gπρm

Surely this means the m isn't canceled out at the end?
 
  • #38
borobeauty66 said:
What I meant by saying the equation was wrong was in your #3 post you put the equation wrong. In actual fact the mass should come after the division. Thus

gif.latex?F%20=%20\frac{4G\pi%20\rho%20}{3}%20m%20r%20\hat{r}.gif


and not

gif.latex?F%20=%20\frac{4G\pi%20\rho%20m}{3}%20r.gif
Those expressions are identical! (Except for the unneeded unit vector.) For the same reason that (a/b)x is the same as (ax/b).
 
  • #39
Doc Al said:
Those expressions are identical! (Except for the unneeded unit vector.) For the same reason that (a/b)x is the same as (ax/b).

ah ok!

thats what confused me, i thought they were different. :-p
 

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