A mass m performs oscillations of period T wh | vedclass

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(D) The time period of a spring-mass system is given by $T = 2\pi \sqrt{\frac{m}{K}}$.Initially,the time period is $T_1 = 2\pi \sqrt{\frac{m}{K}}$.Whe

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$\frac{T}{2}$

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(D) The time period of a spring-mass system is given by $T = 2\pi \sqrt{\frac{m}{K}}$.Initially,the time period is $T_1 = 2\pi \sqrt{\frac{m}{K}}$.When a spring of force constant $K$ is cut into two equal parts,the force constant of each part becomes $K' = 2K$.When these two springs are arranged in parallel,the equivalent force constant $K_{eq}$ is the sum of the individual force constants:$K_{eq} = K' + K' = 2K + 2K = 4K$.The new time period $T_2$ is given by $T_2 = 2\pi \sqrt{\frac{m}{K_{eq}}} = 2\pi \sqrt{\frac{m}{4K}}$.Comparing $T_2$ with $T_1$:$T_2 = \frac{1}{2} 	imes (2\pi \sqrt{\frac{m}{K}}) = \frac{T}{2}$.

$A$ mass $m$ performs oscillations of period $T$ when suspended by a spring of force constant $K$. If the spring is cut into two equal parts and arranged in parallel,and the same mass $m$ is oscillated by them,then the new time period will be:

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