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PhysicsEMI/ACDamped SHM and forced oscillationsMedium2 minPYQ_2019

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A damped harmonic oscillator has a frequency of $5$ oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to $\frac{1}{1000}$ of the original amplitude is close to:

Options:

Answer:

Solution:

$f = 5$
So, $T = \frac{1}{5}$
Time taken for amplitude to drop to half: $10 T = \frac{10}{5} = 2$ s
Now,
$\frac{A_{0}}{1000} = \frac{A_{0}}{{(2)}^{\frac{t}{2}}}$
${(2)}^{\frac{t}{2}} = 1000$
$(\frac{t}{2}) l o g 2 = 3$
$t = \frac{6}{l o g 2} \approx 20 s$

Stream:JEESubject:PhysicsTopic:EMI/ACSubtopic:Damped SHM and forced oscillations

⏱ 2mℹ️ Source: PYQ_2019

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