Angular velocity for a physical pendulum

[NooDota]

Homework Statement

I have a physical pendulum made of a leg which mass is ignored, with a length of 1m, two objects of mass are placed on the bottom and the top of the leg, the first with a mass of m1= m1, and the second with a mass of m2= 3m1, both are L/2 away from the pivot point.

It's swayed to an angle of 60 from the equilibrium position, and left to sway with no initial velocity.

Find the angular velocity the moment it goes through the equilibrium position.

Is there any way to find the angular velocity without using ΔEk a⇒b=∑W(F a⇒b)? I don't want to use that.

Homework Equations

The Attempt at a Solution

 

[Dr. Courtney]

Conservation of energy is the simplest approach.

 

[NooDota]

But the teacher said there is no other possible way to solve it, is this true?

 

[Dr. Courtney]

But the teacher said there is no other possible way to solve it, is this true?

There are other possible ways to solve it, but they may involve math and physics approaches most introductory students (and some teachers) have not learned yet.

 

[NooDota]

Can you name some?

I'm not aiming to actually find the velocity, but to know any other approaches to find it for personal knowledge. I'm not even allowed to use any methods outside the course book, even if they're correct.

 

[Dr. Courtney]

Newton's laws, Lagrangian dynamics, ...

 

[NooDota]

Thanks.

What prior knowledge do I need/should have before learning lagrangian dynamics?

 

[Dr. Courtney]

http://ice.as.arizona.edu/~dpsaltis/Phys422/chapter6.pdf

https://en.wikipedia.org/wiki/Lagrangian_mechanics

http://www.physicsinsights.org/lagrange_1.html