Question:
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:
Correct Option: , 4
Solution:
(4) In damped harmonic oscillation,
$\frac{m d^{2} x}{d t^{2}}=-k x-b v$
$\Rightarrow \frac{m d^{2} x}{d t^{2}}+b \frac{d x}{d t}+k x=0$ ...(1)
In LCR circuit, $\frac{-q}{C}-i R-\frac{L d i}{d t}=0$
$L \frac{d^{2}}{d t^{2}}+R \frac{d q}{d t}+\frac{q}{C}=0$ ...(2)
Comparing equations (i) \& (ii)
$L \leftrightarrow m, C \leftrightarrow \frac{1}{k}, R \leftrightarrow b$