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
AIEEE 2007, Medium
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The two springs are in parallel.
$f=\frac{1}{2 \pi} \sqrt{\frac{K_{1}+K_{2}}{m}}$ $...(i)$
$f^{\prime}=\frac{1}{2 \pi} \sqrt{\frac{4 K_{1}+4 K_{2}}{m}}$
$=\frac{1}{2 \pi} \sqrt{\frac{4\left(K_{1}+4 K_{2}\right)}{m}}=2\left(\frac{1}{2 \pi} \sqrt{\frac{K_{1}+K_{2}}{m}}\right)$
$=2 f \quad$ from eqn. $(i)$
$f=\frac{1}{2 \pi} \sqrt{\frac{K_{1}+K_{2}}{m}}$ $...(i)$
$f^{\prime}=\frac{1}{2 \pi} \sqrt{\frac{4 K_{1}+4 K_{2}}{m}}$
$=\frac{1}{2 \pi} \sqrt{\frac{4\left(K_{1}+4 K_{2}\right)}{m}}=2\left(\frac{1}{2 \pi} \sqrt{\frac{K_{1}+K_{2}}{m}}\right)$
$=2 f \quad$ from eqn. $(i)$
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