The amplitude of a damped oscillator becomes | vedclass

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

Question

(B) The amplitude of a damped oscillator is given by the equation $A = A_0 e^{-\lambda t}$,where $A_0$ is the initial amplitude,$\lambda$ is the dampi

Vedclass · Accepted Answer

$2^3$

Vedclass · Answer

(B) The amplitude of a damped oscillator is given by the equation $A = A_0 e^{-\lambda t}$,where $A_0$ is the initial amplitude,$\lambda$ is the damping constant,and $t$ is time.Given that at $t = 1 	ext{ min}$,the amplitude becomes half:$\frac{A_0}{2} = A_0 e^{-\lambda(1)}$$\frac{1}{2} = e^{-\lambda} \Rightarrow e^{\lambda} = 2$.Now,for $t = 3 	ext{ min}$,the amplitude $A$ is:$A = A_0 e^{-\lambda(3)} = A_0 (e^{-\lambda})^3 = A_0 \left(\frac{1}{e^{\lambda}}ight)^3$Substituting $e^{\lambda} = 2$:$A = A_0 \left(\frac{1}{2}ight)^3 = \frac{A_0}{2^3}$.Comparing this to $\frac{A_0}{X}$,we get $X = 2^3$.

The amplitude of a damped oscillator becomes half in $1 \text{ minute}$. The amplitude after $3 \text{ minutes}$ will be $\frac{1}{X}$ times the original,where $X$ is

Similar Questions

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

The amplitude of a damped oscillator becomes one third in $2 \, s$. If its amplitude after $6 \, s$ is $1/n$ times the original amplitude,then the value of $n$ is

Explain the behaviour of the oscillator when the driving frequency is close to the natural frequency in small damped oscillation and define resonance.

Derive the differential equation for damped oscillations and write its solution.

$A$ block of mass $1 \, kg$ attached to a spring is made to oscillate with an initial amplitude of $12 \, cm$. After $2 \, minutes$ the amplitude decreases to $6 \, cm$. Determine the value of the damping constant $b$ for this motion. (Take $\ln 2 = 0.693$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module