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) In damped oscillation,the amplitude $a$ at time $t$ is given by the formula:$a = a_0 e^{-bt}$where $a_0$ is the initial amplitude and $b$ is the d

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(B) In damped oscillation,the amplitude $a$ at time $t$ is given by the formula:$a = a_0 e^{-bt}$where $a_0$ is the initial amplitude and $b$ is the damping constant.Given that the amplitude becomes half in $1$ minute ($t = 1$ min):$\frac{a_0}{2} = a_0 e^{-b(1)}$$e^{-b} = \frac{1}{2}$We need to find the amplitude after $3$ minutes ($t = 3$ min),which is given as $\frac{a_0}{x}$:$\frac{a_0}{x} = a_0 e^{-b(3)}$$\frac{1}{x} = (e^{-b})^3$Substituting the value of $e^{-b} = \frac{1}{2}$:$\frac{1}{x} = (\frac{1}{2})^3 = \frac{1}{8}$Therefore,$x = 8$.

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

Similar Questions

In forced oscillations,a particle oscillates simple harmonically with a frequency equal to

The amplitude of a damped oscillator becomes $\left(\frac{1}{3}\right)$ of its original amplitude in $2 \ s$. If its amplitude after $6 \ s$ becomes $\left(\frac{1}{n}\right)$ times the original amplitude,the value of $n$ is ($n$ is a non-zero integer).

In damped oscillation,the graph between velocity $(V)$ and position $(x)$ will be:

To understand resonance,describe the experiment of oscillations of five pendulums.

What are damped oscillations?

Vedclass Test Series

Exam Paper Generator

Online Exam Module