Total Energy of a movable pivot-pendulum system, and ω

[Aliasa]

Homework Statement

This is not really a homework questions, just part of my notes confusing me a bit.

This is the derivation of total energy for a pendulum of mass m2 with movable pivot of mass m1.
I don't understand how frequency can be read off. What am I missing?

Homework Equations

See attached screenshot.

The Attempt at a Solution

N/A

 

[Ken G]

You can read off the frequency by noting that the form of the energy looks just like a simple harmonic oscillator. The energy of a simple harmonic oscillator is 1/2 mv^2 + 1/2 kx^2, right? And the oscillation frequency turns out to be the square root of k/m. So that's all that is happening, you just find the coefficient playing the role of k, and the coefficient playing the role of m, and read off the frequency. Form is powerful. (It might help to notice that what we normally call x is here l times phi, and what we normally call v is here l times phi-dot.)