A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring- mass damped oscillator having damping constant b, mass m and oscillating with a force constant k, the correct equivalence will be

A LCR circuit behaves like a damped harmonic oscillator. Comparing it

1.	A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring- mass damped oscillator having damping constant b, mass m and oscillating with a force constant k, the correct equivalence will be
Answer» `L harr k, C harr b, R harr m` `L harr m, C harr (1)/(k), R harr b` `L harr (1)/(b), C harr (1)/(m), R harr (1)/(k)` `L harr m, C harr k, R harr b` Solution :Equation of DAMPED oscillations, `-kx- BV- ma` `:. ma + bv- kx = 0` `:. m= (d^(2)x)/(dt^(2)) + (dx)/(dt) + kx = 0` …(1) Now, for LCR circuit, according to Kirchoff.s second law, `-L (dI)/(dt) - RI -(q)/(c )= 0` `I= (dq)/(dt) " hence" (dI)/(dt) = (d^(2) q)/(dt^(2))` `:. L (d^(2) q)/(dt^(2)) + R (dq)/(dt) + (q)/(a) = 0`...(2) By comparing equation (1) and (2) `L harr m, R harr b, (1)/(C ) harr k`