29.Asystem consists of massless pulley, a spring of force constant k and a block of mass m.If block is just slightly displaced vertically down from its equilibrium position and released , then the period of vertical oscillation is -----

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$L e t i n t h e e q u i l i b i r u m p o s i t i o n x b e t h e e x t e n s i o n i n s t r i n g . T h e t e n s i o n F_{0} i n t h e s p r i n g w i l l b e F_{0} = k x T_{0} = m g, 2 T = k x L e t t h e x' b e t h e d i s p l a c e m e n t o f m a s s m w h e n i t i s s l i g h t l y d o w n w a r d . F = k (x + \frac{x'}{2}) 2 T = k x + k \frac{x'}{2} N e t r e s t o r i n g f o r c e o n m a s s m = T - m g T - T_{0} = k \frac{x'}{4} R e s t o r i n g f o r c e i s p r o p o t i o n a l t o d i s p l a c e m e n t s o m o t i o n i s S . H . M ω = \sqrt{\frac{k / 4}{m}} = \frac{1}{2} \sqrt{\frac{k}{m}}$

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