# Simple pendulum dynamics; equations of motion, work and energy

1. Jul 17, 2012

### xzibition8612

1. The problem statement, all variables and given/known data

See attachment "problem"

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

3. 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, gotta get (1)-(4) right first.

Thanks for the help.

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• ###### problem.doc
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2. Jul 17, 2012

### CWatters

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