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(B) The frequency of oscillation for a mass $m$ connected to a spring with constant $K$ is given by $v = \frac{1}{2\pi} \sqrt{\frac{K}{m}}$.For spring

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$\sqrt{v_1^2 + v_2^2}$

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(B) The frequency of oscillation for a mass $m$ connected to a spring with constant $K$ is given by $v = \frac{1}{2\pi} \sqrt{\frac{K}{m}}$.For springs $S_1$ and $S_2$ with constants $K_1$ and $K_2$ respectively:$v_1 = \frac{1}{2\pi} \sqrt{\frac{K_1}{m}} \implies K_1 = 4\pi^2 v_1^2 m$$v_2 = \frac{1}{2\pi} \sqrt{\frac{K_2}{m}} \implies K_2 = 4\pi^2 v_2^2 m$In the given figure,the mass is connected to two springs in parallel. The effective spring constant is $K_{eff} = K_1 + K_2$.The new frequency $v$ is given by:$v = \frac{1}{2\pi} \sqrt{\frac{K_1 + K_2}{m}}$Substituting the values of $K_1$ and $K_2$:$v = \frac{1}{2\pi} \sqrt{\frac{4\pi^2 v_1^2 m + 4\pi^2 v_2^2 m}{m}}$$v = \frac{1}{2\pi} \sqrt{4\pi^2 (v_1^2 + v_2^2)}$$v = \sqrt{v_1^2 + v_2^2}$

When a mass $m$ is connected individually to two springs $S_1$ and $S_2$,the oscillation frequencies are $v_1$ and $v_2$. If the same mass is attached to the two springs as shown in the figure,the oscillation frequency would be

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