# 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: Option 1) 50 s Option 2) 100 s Option 3) 20 s Option 4) 10 s

Resultant amplitude in damped oscillation -

$A=A_{0}.e^{-\frac{bt}{2m}}$

$E=E_{0}.e^{-\frac{bt}{m}}$

- wherein

$A= Amplitude$

$E= Energy$

$A=A_0e^{-\lambda t}$

$\omega$=5

so $T=\frac{1}{5}$

$10T=\frac{10}{5}=2s$

A=

$A=\frac{A_0}{2}=A_0e^{-\lambda t}$

So $\lambda =\frac{ln2}{2}$

now at time=t $A=\frac{A_0}{1000}$

$\frac{A_{0}}{1000}=A_{0} e^{-\lambda t}$

$e^{-\lambda t}=10^{-3}$

$2^{\frac{t}{2}}=1000$

$\frac{t}{2} \log 2 =3$

$t=\frac{6}{\log 2}\Rightarrow 20s$

Option 1)

50 s

Option 2)

100 s

Option 3)

20 s

Option 4)

10 s

### Preparation Products

##### JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
##### Knockout JEE Main April 2021 (Easy Installments)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
##### Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
##### Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-