Pendulum Amplitude and phase constant

AI Thread Summary
To determine the phase constant and amplitude of a simple pendulum, start by finding the period to calculate the angular frequency (ω). The phase constant (φ) can be derived by using the initial angle at t=0 in the equation θ(t)=Acos(φ). The amplitude (A) represents the maximum displacement, which is 15 degrees in this case. The discussion emphasizes that the specific symbols used in the equations are less important than their mathematical roles. Understanding these concepts allows for a clearer approach to solving the pendulum problem.
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Homework Statement



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?


Homework 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.

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?
 
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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.
 
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?
 
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?
 
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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