Question

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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Answer 1

Correct Answer - A
`k prop (1)/(l)`
Length is halved ,so value of force constant of each part will become `2k`. Now net force constant of `2k` and `2k` as shown in figure will becomes `4k`.
`T = 2pi sqrt ((m)/(k))`
or `T prop (1)/sqrt(k)`
`k` has becomes `4` times. Therefore, `T` will remain half.