# Calculating amplitude of pendulum

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1. Apr 23, 2013

### chicagobears34

1. The problem statement, all variables and given/known data
In a science museum, a 100kg brass pendulum bob swings at the end of a 13.0m -long wire. The pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.7m to the side and releasing it. Because of its compact shape and smooth surface, the pendulum's damping constant is only .010kg/s.

At exactly 12:00 noon, how many oscillations will the pendulum have completed?
And what is its amplitude?
2. Relevant equations
x(t)=Acos(wt)

3. The attempt at a solution
I found the number of oscillations was 1990, but I don't know how to calculate the amplitude?
The period is 7.237seconds so the frequency is .1382
I can say 0=Acos(.1382*3.6185) but that does not help.
how can I solve for amplitude because I do not know the x(t) at any point except that it is 0 at the the lowest point?

2. Apr 23, 2013

### Staff: Mentor

You know the initial amplitude. You also know that energy is being lost over time due to the damping constant. So look up damped harmonic motion (in this case underdamped, since it continues to oscillate but decays over time), and find out how the damping constant relates to the damping ratio and the decaying envelope of the oscillations.

3. Apr 23, 2013

### chicagobears34

The formula be Amax = Ae^(-bt/2m)
A = initial amplitude
b=damping constant
t=time in sec
m=mass in kg

Last edited: Apr 23, 2013
4. Apr 23, 2013

### Staff: Mentor

The damping constant is not quite the same thing as the damping ratio. You want to use the damping ratio in your exponential function.

5. Apr 23, 2013

### rude man

I would ignore the decaying envelope of the oscillations and concentrate on the actual pendulum frequency (which will be a function of the natural frequency, the mass, and the damping constant).

OK I missed the second part which does require amplitude analysis ...
But the first part doesn't ....

Last edited: Apr 23, 2013
6. Apr 23, 2013

### chicagobears34

well, it worked for mastering physics in this particular problem. not sure if it would apply for all damping pendulums