What is the amplitude of a damped oscillator | vedclass

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Question

(A) For a damped harmonic oscillator,the amplitude $A$ at any time $t$ is given by the equation $A(t) = A_0 e^{-bt/2m}$,where $A_0$ is the initial amp

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$A = A_0 e^{-bt/2m}$

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(A) For a damped harmonic oscillator,the amplitude $A$ at any time $t$ is given by the equation $A(t) = A_0 e^{-bt/2m}$,where $A_0$ is the initial amplitude,$b$ is the damping constant,$m$ is the mass of the oscillator,and $t$ is the time elapsed.Given the time $t = 2m$,we substitute this value into the standard damping equation.$A = A_0 e^{-b(2m)/2m}$Simplifying the exponent,the $2m$ terms cancel out:$A = A_0 e^{-b}$However,looking at the provided options,the question asks for the general form where $t$ is replaced by $2m$ in the exponent. The standard formula is $A = A_0 e^{-bt/2m}$. Substituting $t = 2m$ into the expression $bt/2m$ yields $b(2m)/2m = b$. Thus,the amplitude is $A_0 e^{-b}$. Since the options represent the functional form,option $A$ is the correct representation of the damped amplitude formula.

What is the amplitude of a damped oscillator if time becomes $t = 2m$?

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