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(A) In a mechanical system undergoing forced oscillations,the equation of motion is given by $m \frac{d^2x}{dt^2} + b \frac{dx}{dt} + kx = F_0 \cos(\o

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Resistance $(R)$

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(A) In a mechanical system undergoing forced oscillations,the equation of motion is given by $m \frac{d^2x}{dt^2} + b \frac{dx}{dt} + kx = F_0 \cos(\omega t)$,where $b$ is the damping constant.In an $LCR$ series circuit,the differential equation for the charge $q$ is $L \frac{d^2q}{dt^2} + R \frac{dq}{dt} + \frac{q}{C} = V_0 \cos(\omega t)$.Comparing the two equations,we see that the term involving the first derivative of the variable (velocity $\frac{dx}{dt}$ in mechanics and current $I = \frac{dq}{dt}$ in circuits) represents the dissipative element.Therefore,the resistance $R$ in an $LCR$ circuit corresponds to the damping constant $b$ in forced oscillations.

Give the name of the physical quantity in an $LCR$ circuit that corresponds to the damping constant in forced oscillations.

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