# Lab Question - Pendulum

1. Oct 1, 2011

### Icetray

Hi guys,

I was doing my lab report and stumbled onto this question and I would really appriciate it if you guys could assist me on this. (:

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

For a simple pendulum consisting of a mass M attached to a very thin light string of length L, in the absence of air resistance, derive the equation of motion for the simple pendulum in terms of the angular displacement θ relative to its equilibrium position? For “small” oscillation, namely θ is less than 5˚, what is the period T of oscillation? Compare with the derived result in Exercise 4 above.

2. Relevant equations

From Exercise 4:
T = 2π√(I/(MgLg))

3. The attempt at a solution

I'm guessing that I will just be M for a simple pendulum and I'll end up with:
T = 2π√(1/(gLg ))
which doesn't make much sense.

Looking forward to your replies! (:

Last edited: Oct 1, 2011
2. Oct 1, 2011

### Spinnor

What are you using for I?

3. Oct 1, 2011

### Icetray

It's the moment of Inertia of the pendulum (taken to be a I = MLg2.

We assume that the pendulum of mass M is attached to a very light thin string of length Lg.

T = 2π√(Lg/g) but I have no clue how I am to get to this. ):

Last edited: Oct 1, 2011
4. Oct 2, 2011

### Spinnor

I goes as L^2. In your first equation if you substitute for I you should get L in the numerator and not the denominator as you have.

5. Oct 2, 2011

### Icetray

Why does I become L^2? ):

6. Oct 3, 2011

### Icetray

Can anyone assit me with this? ):