# Approximations for small oscillations

1. Jun 29, 2012

### Maybe_Memorie

1. The problem statement, all variables and given/known data

Basically the issue is Landau & Lifgarbagez mechanics says

δl = [r2 + (l + r)2 - 2r(l + r)cosθ]1/2 - l ≈ r(l + r)θ2/2l

2. Relevant equations

θ much less than 1

3. The attempt at a solution

I've no idea how to get the thing on the far right. I'm assuming it's Taylor expansion or something like that but that's not something any of my classes have really explained. Also this isn't homework, I'm on summer holidays.

2. Jun 29, 2012

### clamtrox

Can you massage the formula into
$$\delta l = l \sqrt{1 + \frac{2r(l+r)}{l^2}(1-\cos \theta)} - l$$? Then all you need to do is to do Taylor expansions for 1-cos θ and √(1+x).

3. Jun 29, 2012

### Staff: Mentor

try using the cos(theta)= 1 - (theta^2)/2 approx for small angles in radians