(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a system of one generalized coordinate theta, having the following Lagrangian equation of motion:

r and b are constants

m is mass

(1/3)mb[tex]^{2}[/tex][tex]\ddot{\theta}[/tex] = r(r+b)[tex]\theta[/tex] + r[tex]^{2}[/tex][tex]\theta[/tex][tex]^{3}[/tex] + gr[tex]\theta[/tex]

And this potential energy (if it matters):

U = mg(r+b) - mgr[tex]\theta[/tex][tex]^{2}[/tex]

There is an equilibrium point where theta is equal to zero.

Find the angular frequency of small oscillations about [tex]\theta[/tex] = 0.

2. Relevant equations

3. The attempt at a solution

Using the potential energy, can't I just say

U = (1/2)k[tex]\theta[/tex][tex]^{2}[/tex]

where

k = 2mgr

so that I can write

[tex]\omega[/tex] = (k/m)^(1/2)

[tex]\omega[/tex] = (2gr)^(1/2)

and call that the angular frequency?

But the problem asks me to do it the Lagrangian way.

So

[tex]\omega[/tex] = (2[tex]\pi[/tex])/[tex]\tau[/tex]

How can I find tau?

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# Homework Help: Finding Angular Frequency of Small Oscillations about an Equilibrium

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