As per given figures, two springs of spring c | vedclass

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Question

For figure $(a):$

$K _{	ext {oq }}=\frac{ K 	imes 2 K }{ K +2 K }=\frac{2 K }{3}$

$T =2 \pi \sqrt{\frac{ m }{ K _{ eq }}}=2 \pi \sqrt{\frac{ m

Vedclass · Accepted Answer

$2$

Vedclass · Answer

For figure $(a):$

$K _{	ext {oq }}=\frac{ K 	imes 2 K }{ K +2 K }=\frac{2 K }{3}$

$T =2 \pi \sqrt{\frac{ m }{ K _{ eq }}}=2 \pi \sqrt{\frac{ m }{2 K / 3}}=2 \pi \sqrt{\frac{3 m }{2 K }}$

For figure $(b):$

$K _{ eq }=3 K , T ^{\prime}=2 \pi \sqrt{\frac{ m }{3 K }}$

$\frac{ T ^{\prime}}{ T }=\sqrt{\frac{ m 	imes 2 K }{3 K 	imes 3 m }}=\frac{\sqrt{2}}{3}$

$T ^{\prime}=\sqrt{2}$

$x =2$

As per given figures, two springs of spring constants $K$ and $2\,K$ are connected to mass $m$. If the period of oscillation in figure $(a)$ is $3 s$, then the period of oscillation in figure $(b)$ will be $\sqrt{ x }$ s. The value of $x$ is$.........$

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