Question

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Solution

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Correct option is D)

$dt_{2}d_{2}x +(2mk 2x mk )dtdx +(mk )_{2}x=0$

$⇒dt_{2}d_{2}x +2τw_{0}dtdx +w_{0}x=0 $

$τ=2mk c ⇒$ damping ratio $c=b⇒$ damping constant

$W_{0}=mk ⇒$ angular frequency

$⇒dt_{2}d_{2}x +(mb )dtdx +(mk )x=0 $..........(1)

For LCR circuit

use KVL:-

$V−LdtdI −IR−cq =0$

$⇒dt_{2}d_{2}q +LR dtdq +(LC1 )q=LV $...........(2) $I=dtdq $

By comparing (1) and (2):=

$L→m,R→b,LC→km $

$⇒C→k1 $

option (D) is correct.

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