In figure (A),mass '2m' is fixed on mass 'm' | vedclass

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Question

(A) For figure $(A)$,the total mass is $M = m + 2m = 3m$. The two springs of constant $k$ are in parallel,so the effective spring constant is $k_{eff}

Vedclass · Accepted Answer

$\frac{T_{1}}{T_{2}}=\frac{3}{\sqrt{2}}$

Vedclass · Answer

(A) For figure $(A)$,the total mass is $M = m + 2m = 3m$. The two springs of constant $k$ are in parallel,so the effective spring constant is $k_{eff} = k + k = 2k$.The time period is $T_{1} = 2\pi \sqrt{\frac{M}{k_{eff}}} = 2\pi \sqrt{\frac{3m}{2k}}$.For figure $(B)$,the mass is $m$. The two springs of constants $k$ and $2k$ are in parallel,so the effective spring constant is $k_{eff} = k + 2k = 3k$.The time period is $T_{2} = 2\pi \sqrt{\frac{m}{3k}}$.Taking the ratio,we get:$\frac{T_{1}}{T_{2}} = \frac{2\pi \sqrt{\frac{3m}{2k}}}{2\pi \sqrt{\frac{m}{3k}}} = \sqrt{\frac{3m}{2k} \cdot \frac{3k}{m}} = \sqrt{\frac{9}{2}} = \frac{3}{\sqrt{2}}$.

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