A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be:

Engineering

Physics

L C Oscillation and LCR Damped Oscillation

Question

L $\leftrightarrow$ k, C $\leftrightarrow$ b, R $\leftrightarrow$ m

$L \leftrightarrow \frac{1}{b}, C \leftrightarrow \frac{1}{m}, R \leftrightarrow \frac{1}{k}$

L $\leftrightarrow$ m, C $\leftrightarrow$ k, R $\leftrightarrow$ b

$L \leftrightarrow m, C \leftrightarrow \frac{1}{k}, R \leftrightarrow b$

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In damped oscillation

ma + bv + kx = 0

$m \frac{d^{2} x}{{dt}^{2}} + b \frac{dx}{dt} + kx = 0$ ….(i)

In the circuit

$- iR - L \frac{di}{dt} - \frac{q}{c} = 0$

$L \frac{d^{2} q}{{dt}^{2}} + R \frac{dq}{dt} + \frac{1}{c} . q = 0$ …..(ii)

Comparing equation (i) and (ii)

$m = L, b = R, k = \frac{1}{c}$