Oscillations

JEE Main level, single correct, medium

47 of 194

Question 47 of 194

A damped harmonic oscillator has a frequency of 55 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to 11000\dfrac{1}{1000} of the original amplitude is close to:

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Answer: (C) 20s20s

f=5f=5
So, T=15T=\dfrac{1}{5}
Time taken for amplitude to drop to half: 10T=105=210T=\dfrac{10}{5}=2 s
Now,
A01000=A0(2)t2\dfrac{{A}_{0}}{1000}=\dfrac{{A}_{0}}{{(2)}^{\dfrac{t}{2}}}
(2)t2=1000{(2)}^{\dfrac{t}{2}}=1000
(t2)log2=3\left(\dfrac{t}{2}\right)log2=3
t=6log2≈20st=\dfrac{6}{log2}\approx 20 s

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