An object suspended from a spring exhibits oscillations of period T. Now, the spring is cut in half and the two halves are used to support the same object, as shown in figure. Show that the new period of oscillation is T/2.

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Solution

$k \propto \frac{1}{l}$
Length is halved, so value of force constant of each part will become 2k. Now net and 2k as shown In figure will becomes 4k.
$T = 2 π \sqrt{\frac{m}{k}}$
or $T \propto \frac{1}{\sqrt{k}}$
k has becomes 4 times. Therefore T will remain half.

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An object suspended from a spring exhibits oscillations of period T. Now, the spring is cut in half and the two halves are used to support the same object, as shown in figure. Show that the new period of oscillation is T/2.

k∝1lLength is halved, so value of force constant of each part will become 2k. Now net and 2k as shown In figure will becomes 4k.T=2π√mkor T∝1√kk has becomes 4 times. Therefore T will remain half.

$k \propto \frac{1}{l}$
Length is halved, so value of force constant of each part will become 2k. Now net and 2k as shown In figure will becomes 4k.
$T = 2 π \sqrt{\frac{m}{k}}$
or $T \propto \frac{1}{\sqrt{k}}$
k has becomes 4 times. Therefore T will remain half.