Pendulum amplitude after 5 minutes

In summary, two pendulums, one with an aluminum bob and one with a brass bob, are set into oscillation with the same amplitude and length. After 5 minutes, the aluminum pendulum is oscillating with half its initial amplitude. The oscillation amplitude of the brass pendulum is 0.81 times the initial amplitude. The damping ratio and Q factor may be helpful in understanding this problem.
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Suppose one pendulum consists of a 1-meter string with a bob that is an aluminum sphere 2 inches in diameter. A second pendulum consists of a 1-meter string with a bob that is a brass sphere 2 inches in diameter. The two pedulums are set into oscillation at the same time and with the same amplitude A. After 5 minutes of undisturbed oscillation, the aluminum pendulum is oscillating with one half of its initial amplitude. What is the oscillation amplitude of the brass pendulum? Assume that the friction is due to the relative velocity of bob and air and that the instantaneous rate of energy loss is proportional to the square of the velocity of the bob.

The answer is supposed to be .81A.


y(t) = Ae^(t/2[tex]\tau[/tex])cos([tex]\omega[/tex]t)


I think I might just be confused about the wording of this problem. I know that the angular frequency of a pendulum only depends on gravity and the length of the string, therefore both pendulums will be exactly the same. So now I tried to plug in 300 seconds to the above equation for t, and set A to .5A. Now I am stuck, I don't know how to get [tex]\tau[/tex].

Also, this is where my confusion comes in, if after 5 minutes the aluminum bob is oscillating at half its initial amplitude, wouldn't the brass bob be the exact same? Then the answer would be .5A.
 
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What is a pendulum amplitude?

A pendulum amplitude is the maximum displacement of a pendulum from its equilibrium or resting position.

How is pendulum amplitude measured?

Pendulum amplitude can be measured by determining the distance between the lowest point of the pendulum's swing and its equilibrium position.

What factors affect the pendulum amplitude?

The pendulum amplitude can be affected by the length of the pendulum, the mass of the pendulum bob, and the force of gravity.

What is the relationship between pendulum amplitude and time?

The pendulum amplitude decreases over time due to the effects of friction and air resistance.

How does pendulum amplitude change after 5 minutes?

The pendulum amplitude will decrease slightly after 5 minutes due to the effects of friction and air resistance, but the change will be minimal.

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