Suppose one pendulum consists of a 1-meter string with a bob that is an aluminum

Question

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.

Explanation / Answer

    Since, time period of the pendulum is indepedent of Nature of the bob or material with which it is maden. As the defination & formula of . Time period , time required to complete 1 ocsillation   is the time period Time period of the pendulum is only depend upon its lenght , it doesn't depends upon its nature or material with which it is prefared Thus, after 5  min. both will have same Amplitude i.e brass pendulum will also have the same Amplitude   

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