The amplitude of a damped harmonic oscillator | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The amplitude of a damped harmonic oscillator is given by $A(t) = A_0 e^{-bt}$.Given that the amplitude becomes half in $3 \ s$:$A(3) = A_0 e^{-3b

Vedclass · Accepted Answer

$2^3$

Vedclass · Answer

(C) The amplitude of a damped harmonic oscillator is given by $A(t) = A_0 e^{-bt}$.Given that the amplitude becomes half in $3 \ s$:$A(3) = A_0 e^{-3b} = \frac{A_0}{2}$$e^{-3b} = \frac{1}{2} \quad \dots (i)$In the next $6 \ s$,the total time elapsed is $3 \ s + 6 \ s = 9 \ s$. The amplitude at $t = 9 \ s$ is:$A(9) = A_0 e^{-9b} = A_0 (e^{-3b})^3$Substituting equation $(i)$ into the expression:$A(9) = A_0 \left(\frac{1}{2}\right)^3 = A_0 \left(\frac{1}{8}\right)$Since the amplitude becomes $1/x$ of the initial amplitude,we have $1/x = 1/8$,which means $x = 8 = 2^3$.Therefore,the correct option is $C$.

The amplitude of a damped harmonic oscillator becomes half in $3 \ s$ and will become $1/x$ of the initial amplitude in the next $6 \ s$,where $x$ is:

Similar Questions

Which of the following statements regarding the damping force of a damped oscillator is $NOT$ correct?

$A$ steady force of $120 \ N$ is required to push a boat of mass $700 \ kg$ through water at a constant speed of $1 \ m/s$. If the boat is fastened by a spring and held at $2 \ m$ from the equilibrium position by a force of $450 \ N$,find the angular frequency of damped $SHM$ in $rad/s$.

$A$ particle is performing simple harmonic motion. If the oscillations are damped oscillations,then the angular frequency is given by:

In case of a forced vibration,the resonance wave becomes very sharp when the:

In damped $SHM$,the $SI$ unit of damping constant is

Vedclass Test Series

Exam Paper Generator

Online Exam Module