Calculating amplitude of pendulum

In summary, a 100kg brass pendulum bob swings at a science museum, starting at 8:00 a.m. each morning by pulling it 1.7m to the side and releasing it. Its damping constant is .010kg/s and at 12:00 noon, it will have completed 1990 oscillations. To calculate its amplitude, one can use the formula Amax = Ae^(-bt/2m) where A is the initial amplitude, b is the damping constant, t is time in seconds, and m is the mass in kilograms. It is important to note that the damping constant is not the same as the damping ratio, and one should use the damping ratio in the exponential function for more accurate
  • #1
chicagobears34
37
0

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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  • #2
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
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:
  • #4
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
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:
  • #6
well, it worked for mastering physics in this particular problem. not sure if it would apply for all damping pendulums
 

Related to Calculating amplitude of pendulum

1. How do I calculate the amplitude of a pendulum?

The amplitude of a pendulum can be calculated by measuring the maximum displacement of the pendulum from its equilibrium position. Alternatively, you can use the equation A = θmax - θmin, where A is the amplitude and θmax and θmin are the maximum and minimum angles of the pendulum, respectively.

2. What is the formula for calculating the amplitude of a pendulum?

The formula for calculating the amplitude of a pendulum is A = θmax - θmin, where A is the amplitude and θmax and θmin are the maximum and minimum angles of the pendulum, respectively.

3. Can the amplitude of a pendulum be negative?

Yes, the amplitude of a pendulum can be negative. This occurs when the pendulum swings past its equilibrium position in the opposite direction.

4. How does the length of a pendulum affect its amplitude?

The length of a pendulum does not affect its amplitude. The amplitude is solely determined by the maximum displacement of the pendulum from its equilibrium position.

5. Why is it important to calculate the amplitude of a pendulum?

Calculating the amplitude of a pendulum is important in understanding the behavior of the pendulum and how it is affected by different variables such as length, mass, and gravitational force. It also allows for the prediction of the pendulum's motion and can help in designing and optimizing pendulum-based devices such as clocks and metronomes.

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