Calculating amplitude of pendulum

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Homework Help Overview

The problem involves a brass pendulum bob with a mass of 100 kg, suspended by a 13.0 m wire, which is released from an initial displacement of 1.7 m. The discussion centers on calculating the number of oscillations completed by the pendulum by noon and determining its amplitude, considering the effects of damping.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relationship between the damping constant and the amplitude of oscillations, referencing damped harmonic motion. There are attempts to connect the initial amplitude with the damping effects over time, and questions arise regarding the application of formulas related to amplitude decay.

Discussion Status

Some participants have provided insights into the relationship between the damping constant and amplitude, suggesting that the original poster consider the effects of damping on the oscillations. There is an acknowledgment of the need to clarify the distinction between the damping constant and the damping ratio, indicating a productive exploration of the topic.

Contextual Notes

The discussion includes references to specific formulas and concepts related to damped harmonic motion, but there is a lack of consensus on the best approach to calculate the amplitude in this context. Participants are navigating through the implications of damping on the pendulum's behavior.

chicagobears34
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Homework Statement


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?

Homework Equations


x(t)=Acos(wt)


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?
 
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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.
 
gneill said:
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.

The formula be Amax = Ae^(-bt/2m)
A = initial amplitude
b=damping constant
t=time in sec
m=mass in kg
 
Last edited:
The damping constant is not quite the same thing as the damping ratio. You want to use the damping ratio in your exponential function.
 
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 ... :redface:
But the first part doesn't ...
 
Last edited:
well, it worked for mastering physics in this particular problem. not sure if it would apply for all damping pendulums
 

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