# Determine an expression for the period of motion.

1. Dec 3, 2011

### borobeauty66

problem solved, thanks

Last edited: Dec 3, 2011
2. Dec 3, 2011

### Staff: Mentor

I'm not understanding the problem. You have the equation you need, just change r to x. What would k be?

The real question is: Can you solve it to find the period? (Compare it to the equations for simple harmonic motion.)

FYI: Writing your equations using Latex will make things easier:
$$F = - \frac{4G\pi\rho m}{3} r$$

Last edited: Dec 3, 2011
3. Dec 3, 2011

### borobeauty66

k is the force constant.

4. Dec 3, 2011

### Staff: Mentor

Sure, so in your equation what would it be?

5. Dec 3, 2011

### borobeauty66

k = mω^2

We haven't been given the values for anything, we're supposed to find the expression in a format of algerbra only.

6. Dec 3, 2011

### Staff: Mentor

That's the solution for the usual simple harmonic motion equation. Since your equation (for gravity) has the same form, it will have the same solution. Compare the two equations you wrote before: What will take the place of 'k' in your equation?
Right.

7. Dec 3, 2011

### borobeauty66

Do you mean F = -kx

and

k = mω^2

Therefore

F = -mw^2 x

8. Dec 3, 2011

### Staff: Mentor

I mean to take that equation and compare it to the one you wrote for your gravity problem. What would be the equivalent to k?

9. Dec 3, 2011

### borobeauty66

OK give me a few minutes. I'm not very quite when it comes to rearranging and combing equations.

10. Dec 3, 2011

### Staff: Mentor

You shouldn't have to rearrange anything, just read it off.

Your equation has the form: Force = (some constant) x, what's that constant? (It's much easier than you think!)

11. Dec 3, 2011

### borobeauty66

I'm over-complcating things then?

I've just got to pop out anyway, so I'll have a think about it.

12. Dec 3, 2011

### Staff: Mentor

I'd say so. You know the solution for the standard SHM problem of a mass on a spring. So you want to compare the equations, since the same equations have the same solutions.

13. Dec 3, 2011

### borobeauty66

Not sure if my thinking is correct.

k = 4Gπρ/3

14. Dec 3, 2011

### Staff: Mentor

Almost! (You left out the mass.) But that's exactly the right idea.

15. Dec 3, 2011

### borobeauty66

Oh yes, mass sorry, so,

k = 4Gπρm/3

Ok, i'm with you up to hear, just unsure how this applies to period of motion, which is what the question asks for.

16. Dec 3, 2011

### Staff: Mentor

Well, what's the period for the standard SHM equation? (In terms of k.)

17. Dec 3, 2011

### borobeauty66

You mean the frequency? ω?

18. Dec 3, 2011

### Staff: Mentor

Well, you want the period. But you can express the period in terms of the frequency.

19. Dec 3, 2011

### borobeauty66

Oh I see, the period, t.

So, since ω = 2π/t

t =2π/ω (is this correct? as i say, i'm terrible as rearranging equations)

Not sure where to go from here.

20. Dec 3, 2011

### Staff: Mentor

Good.

Now use the expression for ω.