A) \[L\leftrightarrow m,C\leftrightarrow \frac{1}{k},R\leftrightarrow b\]
B) \[L\leftrightarrow k,C\leftrightarrow b,R\leftrightarrow m\]
C) \[L\leftrightarrow \frac{1}{b},C\leftrightarrow \frac{1}{m},R\leftrightarrow \frac{1}{k}\]
D) \[L\leftrightarrow m,C\leftrightarrow k,R\leftrightarrow b\]
Correct Answer: A
Solution :
[a] |
In damped oscillation, |
\[\frac{m{{d}^{2}}x}{d{{t}^{2}}}=-kx-bv\] |
\[\Rightarrow \frac{m{{d}^{2}}x}{d{{t}^{2}}}+b\frac{dx}{dt}+kx=0...(i)\] |
In LCR circuit, \[\frac{-q}{C}-iR-\frac{Ldi}{dt}=0\] |
\[L\frac{{{d}^{2}}q}{d{{t}^{2}}}+R\frac{dq}{dt}+\frac{q}{C}=0\] |
\[\therefore m\equiv L,b\equiv R,k\equiv \frac{1}{C}\] |
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