A pendulum with time period of `1s` is losing energy due to damping. At time its energy is `45 J`. If after completing `15` oscillations, its energy has become `15 J`. Its damping constant (in `s^(-1)`) is :-

Options

A. `(1)/(30)in3`
B. `(1)/(15)in3`
C. 2
D. `(1)/(2)`

Answer

A

Explanation

T = 1 second
For damping amplitude,
`A = A_(0)e^(-bt)`
One oscillation take 1 second, 15 oscillations
take time t = 15 seconds `therefore sqrt(E ) = sqrt(E_(0))e^(-bt)`
`sqrt(15) = sqrt(45) e^(-(15))`
`(1)/(sqrt(3)) = e^(-b(15))`
`(3)^((-1)/(2)) = e^(-15b)`
`(1)/(2)"In" 3 = 15b rArr b = ("In3")/(30)`