question_answer

A pendulum with time period of 1s is losing energy due to damping. At certain time its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, its damping constant (in\[{{s}^{-1}}\]) is:   [JEE MAIN 11-04-2015]

A) \[\frac{1}{30}\ln 3\]      

B)      \[\frac{1}{15}\ln 3\]

C)  2                    

D)      \[\frac{1}{2}\]

Correct Answer: A

Solution :

[a] Amplitude in a damped oscillation is given by  energy

where  is initial energy

on taking log both sides