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(A) In the given figure,the mass $m$ is connected between two springs. When the mass is displaced,one spring is compressed while the other is stretche

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$2f$

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(A) In the given figure,the mass $m$ is connected between two springs. When the mass is displaced,one spring is compressed while the other is stretched. This configuration is equivalent to a parallel combination of springs.The effective spring constant $k_{eff}$ for springs in parallel is given by:$k_{eff} = k_1 + k_2$The frequency of oscillation $f$ is given by:$f = \frac{1}{2\pi} \sqrt{\frac{k_{eff}}{m}} = \frac{1}{2\pi} \sqrt{\frac{k_1 + k_2}{m}} \quad ...(1)$If both $k_1$ and $k_2$ are made four times their original values,the new spring constants are $k_1' = 4k_1$ and $k_2' = 4k_2$. The new effective spring constant $k_{eff}'$ is:$k_{eff}' = 4k_1 + 4k_2 = 4(k_1 + k_2)$The new frequency $f'$ is:$f' = \frac{1}{2\pi} \sqrt{\frac{k_{eff}'}{m}} = \frac{1}{2\pi} \sqrt{\frac{4(k_1 + k_2)}{m}}$$f' = 2 	imes \left( \frac{1}{2\pi} \sqrt{\frac{k_1 + k_2}{m}} ight)$$f' = 2f$

Two springs,of force constants $k_1$ and $k_2$,are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$. If both $k_1$ and $k_2$ are made four times their original values,the frequency of oscillation becomes

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