Simple pendulum dynamics; equations of motion, work and energy

[xzibition8612]

Homework Statement

See attachment "problem"

Homework Equations

Euler's laws of motion (moment equations), work and energy equations

The Attempt at a Solution

See attachment "work"

I did the work for (1) and (2). I end up with two equations: the first is the tension T, the second is the angular acceleration. I'm not so sure if I made any mistakes in solving the equations of motion, but I'm not really comfortable with these two equations and feel like something went wrong. I just can't see it. Remember the pendulum is a point mass, hence for the point mass the moment of inertia is ml^2. Now for question (3), how do I find the angular velocity? None of my two equations contain this quantity, hence I feel like something went wrong. For (4), I do indeed have T= 9.83/sin(theta). Now how do I plot this in relation to time? Because from this equation I can only plot the tension T in relation to the change in angle, not time. I'm not going to worry about (5) right now, got to get (1)-(4) right first.

Thanks for the help.

 

[CWatters]

Perhaps look at it from the point of view of energy eg KE at the bottom = PE at the top.