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Option d
Explanation:
In the case of damped vibration, amplitude at any in_stant t us given by
a = ao e^-bt
Where,
ao = initial amplitude
b = damping constant
CASE I
t = 100 T and a = ao / 3
ao / 3 = ao e^-b ( 100 T )
=> e^-100 bt = 1/3
=> e^-100 bT = 1/3
CASE II
t = 200 T
a = ao e^-bt = ao e^-b ( 200 T )
a = ao ( e^-100 bT )^2 = ao × [ 1/3 ]^2
a = ao / 9
Thus, after 200 oscillations, amplitude will become 1/9 times!
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