An object suspended from a spring exhibits oscillations of period T. Now the spring is cut in two halves and the same object is suspended with two halves as shown in figure. The new time period of oscillation will become:

$\frac{T}{\sqrt{2}}$

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$2 T$

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$\frac{T}{2}$

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$\frac{T}{2 \sqrt{2}}$

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Solution

The correct option is C
$\frac{T}{2}$

Force constant of a spring $\propto \frac{1}{l e n g t h o f s p r i n g}$
i.e., the force constant of two halves will become 2k each. (k = force constant of complete spring)
$∴ k_{e f f} = 2 k + 2 k = 4 k T \propto \frac{1}{\sqrt{k}}$
i.e., $T^{'} = \frac{T}{2}$

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An object suspended from a spring exhibits oscillations of period T. Now the spring is cut in two halves and the same object is suspended with two halves as shown in figure. The new time period of oscillation will become:

The correct option is C T2 Force constant of a spring ∝1length of spring i.e., the force constant of two halves will become 2k each. (k = force constant of complete spring) ∴keff=2k+2k=4kT∝1√k i.e., T′=T2