As shown in the figure,S_1 and S_2 are identi | vedclass

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(C) In the initial configuration,the mass $m$ is connected to two springs in parallel. The effective spring constant is $K_{eff} = K + K = 2K$.The fre

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$\frac{f}{\sqrt{2}}$

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(C) In the initial configuration,the mass $m$ is connected to two springs in parallel. The effective spring constant is $K_{eff} = K + K = 2K$.The frequency of oscillation is given by $f = \frac{1}{2\pi} \sqrt{\frac{K_{eff}}{m}} = \frac{1}{2\pi} \sqrt{\frac{2K}{m}}$.When spring $S_2$ is removed,only one spring with spring constant $K$ remains.The new effective spring constant is $K'_{eff} = K$.The new frequency of oscillation is $f' = \frac{1}{2\pi} \sqrt{\frac{K}{m}}$.Comparing $f'$ and $f$,we have $\frac{f'}{f} = \frac{\frac{1}{2\pi} \sqrt{\frac{K}{m}}}{\frac{1}{2\pi} \sqrt{\frac{2K}{m}}} = \frac{1}{\sqrt{2}}$.Therefore,$f' = \frac{f}{\sqrt{2}}$.

As shown in the figure,$S_1$ and $S_2$ are identical springs with spring constant $K$ each. The oscillation frequency of the mass $m$ is $f$. If the spring $S_2$ is removed,the oscillation frequency will become

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