The amplitudes of a damped harmonic oscillato | vedclass

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

Question

(A) For a damped harmonic oscillator,the amplitude at time $t$ is given by $A(t) = A_0 e^{-bt}$,where $A_0$ is the initial amplitude and $b$ is the da

Vedclass · Accepted Answer

$A_1 = \sqrt{A_0 A_2}$

Vedclass · Answer

(A) For a damped harmonic oscillator,the amplitude at time $t$ is given by $A(t) = A_0 e^{-bt}$,where $A_0$ is the initial amplitude and $b$ is the damping constant.At $t = 2 \ s$,$A_1 = A_0 e^{-2b} \implies \frac{A_1}{A_0} = e^{-2b}$.At $t = 4 \ s$,$A_2 = A_0 e^{-4b} \implies \frac{A_2}{A_0} = e^{-4b}$.We can write $e^{-4b} = (e^{-2b})^2$.Substituting the expression for $e^{-2b}$,we get $\frac{A_2}{A_0} = \left(\frac{A_1}{A_0}\right)^2$.$\frac{A_2}{A_0} = \frac{A_1^2}{A_0^2}$.$A_2 = \frac{A_1^2}{A_0}$.$A_1^2 = A_0 A_2 \implies A_1 = \sqrt{A_0 A_2}$.

The amplitudes of a damped harmonic oscillator after $2 \ s$ and $4 \ s$ are $A_1$ and $A_2$ respectively. If the initial amplitude of the oscillator is $A_0$,then

Similar Questions

What is resonance? Give its example.

The amplitude of a wave is represented by $A = \frac{c}{a + b - c}$. Resonance will occur when:

When two violin wires with different fundamental frequencies are vibrated to play some music,can they produce resonance?

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

Two damped spring-mass oscillating systems have identical spring constants and decay times. However,system $A$'s mass $m_A$ is twice system $B$'s mass $m_B$. How do their damping constants,$b$,compare?

Vedclass Test Series

Exam Paper Generator

Online Exam Module