# Pendulum Amplitude and phase constant

1. Dec 13, 2011

### soccerscholar

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

A simple pendulum of length 1m with bob mass 125g is pulled 15 degrees to the right and released at t=0.What are the phase constant and amplitude?

2. Relevant equations

θ(t)=Acos(ζt+phi) ---> my teacher gave us a weird symbol that I've never seen before, it has always been ω instead of ζ on classwork and such.

3. The attempt at a solution

I am just completely lost with how to even start this. My teacher doesn't explain anything, he basically gives us in-class problems that have nothing to do with the homework he assigns. Can someone explain how amplitude and phase constant can be found?

2. Dec 13, 2011

### Delphi51

I once had a Japanese prof who ran out of English and Greek letters, so he started using Japanese ones. Don't let it bother you; remember Feynman said the names don't matter.

Why not find the period first? Then you can get the ω easily. And figure out what phi you need to make it fit the angle at time zero.

3. Dec 13, 2011

### Simon Bridge

The weird symbol "ζ" is "zeta", the seventh letter of the Greek alphabet. The actual symbols don't matter - it is their roles that count.
(I once ran out of letters and resorted to geometric shapes.)

The phase is $\phi$. To find it, consider what the amplitude is at t=0 in your experiment and in the equation.

$\zeta = 1/ 2\pi T$ ... which is, of course, the angular frequency. I figure you can find the period of a pendulum OK?

4. Dec 13, 2011

### soccerscholar

Wow, it's really that simple? Thanks, I really understand this a lot better.

So to find phi, do I use θ(0)=Acos(phi), plug in the initial angle it was pulled back for the theta0, and solve for phi?

5. Dec 13, 2011

### Simon Bridge

Careful - you have two variables, the phi and the A.
The A is the amplitude. The phi modifies the start value because you may not start time exactly when the swing is at it's maximum displacement.

If the equation was a sign instead of a cosine, phi would be different.

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