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JEE Main 20198 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
8 April
Shift
Evening Shift
Subject
Physics
Chapter
Oscillations

JEE Main 2019 · 8 April · Evening Shift · Physics · Oscillations

A damped harmonic oscillator has a frequency of 5 oscillations per...

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:

Options

  1. A50s50s
  2. B100s100s
  3. C20s20s
  4. D10s10s

Correct answer

C. 20s20s

Step-by-step solution

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
\left(\dfrac{t}{2}\right)\log 2 = 3<br/><br/>t = \dfrac{6}{\log 2} \approx 20s
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