# Help with Godstein Chapter 3

1. Dec 11, 2013

### ASmc2

This is a question to those who have the 3rd edition at their disposal. Where do 3.45 and 3.46 come from? I understood everything he said before that...

2. Dec 12, 2013

### voko

Start with equ. 3.34, an linearize it about $u = u_0$. You will get an equation for simple harmonic motion, from which those two equations will follow.

3. Dec 12, 2013

### ASmc2

I get an equation of the form x''+kx=c. where c is some constant, '' gives the second derivative with respect to theta, and x is u-u0.

4. Dec 12, 2013

### voko

You are on the right track, but you should have obtained $x'' + kx = 0$. You made a mistake somewhere. Without seeing your work, I can't say what it was.

5. Dec 12, 2013

### ASmc2

My work is attached.

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6. Dec 12, 2013

### ASmc2

That u0^3 and u0 terms bother me, as you can see.

7. Dec 13, 2013

### voko

The very first equation you have is incorrect. $${d \over du} V \left( \frac 1 u \right) \ne f(u)$$ Which is actually strange, because the third equation could only have been obtained if you had differentiated that correctly.

8. Dec 13, 2013

### ASmc2

OK, I get that now, thanks. I got the correct equation now. Now to get (3.46).

9. Dec 13, 2013

### voko

3.46 should follow from what you got immediately: $\ddot x + \beta^2 x = 0$.

10. Dec 14, 2013

### ASmc2

Yes. Thanks for the help with 3.45