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

Obtain the differential equation of forced oscillation.

The amplitude of a damped oscillator varies with time as $A(t) = A_0 \exp(-bt / 2m)$, where $b = 70 \text{ g/s}$ and $m = 200 \text{ g}$. How long does it take for the mechanical energy to drop to one-fourth of its initial value (in $s$)? (Take $\ln 2 = 0.7$)

What are damped oscillations?

Which of the diagrams shown in the figure represents the variation of total mechanical energy of a pendulum oscillating in water as a function of time?

Vedclass Test Series

Exam Paper Generator

Online Exam Module