Different methods of finding the weight-work in a pendulum

[NooDota]

Homework Statement

In a physical, or a simple pendulum, to get the velocity of the pendulum at some point, we apply the kinetic energy theory, and use m*g*h to calculate the work done by weight, I'm wondering if there are any other ways to calculate the work? I don't care how complicated it is, I'm just curious. Can I use W = F.d?

D in this case would be the circular sector, correct? I think there's some law to calculate that, I can't recall exactly, it's something like 1/2 * r * omega^2

But how would I get the weight component?

Here's a sample problem (I translated it myself, so the notation may not be fine), the first 3 questions are irrelevant, it's the 4th one where you use W=m*g*h

A physical pendulum is made up by a rod with neglected mass which has a length of 1m, carrying on its upper end a particle with a mass of 0.2kg, and its on lower end, a particle with a mass of 0.6kg, the rod oscillates around a horizontal axis going through the half of it (center of mass).

1. Find the period for small oscillations.
2. Calculate the length of the simple pendulum that has the same period as the previous pendulum.
3. Find the period of the pendulum if it were to oscillate with an amplitude of 0.4rad
4. We sway the rod from its balance point to an angle of 60 degrees and leave it with zero initial velocity.
A. Find the velocity of the pendulum the moment it goes through the balance point.

I'm not interested in a solution, all I want to know if it's possible to calculate the work of the weight force without m*g*h*, or even finding the velocity without resorting to the kinetic energy theorem.

Thanks

Homework Equations

The Attempt at a Solution

 

[J Hann]

I don't know why you would want to do that, but simply
m g sin (theta) is the restoring force along the arc of the pendulum
and R d (theta) is the differential displacement.
This simply integrates to the potential energy.

 

[NooDota]

Yeah, how exactly does it go back to m*g*h?

Is there any other way? The only reason I'm asking is because I'm curious, that's all.

 

[J Hann]

When you integrate should get [R - R cos (theta)] which is
just h the height of the mass of the pendulum and thus the
potential energy.