A ball of mass m kept at the centre of a string of length `L` is pulled from centre in perpendicular direction and released. Prove that motion of ball is simple harmonic and determine time period of oscillation
Text Solution
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Restoring force `F = -2Tsintheta` When `theta` is small `sintheta ~~ tantheta ~~ theta = (x)/(L//2)` `m(d^(2)x)/(dt^(2))= - 2Tsintheta = -2Ttheta = -2T(x)/(L//2)` `(d^(2)x)/(dt^(2)) = (4T)/(mL) xx rArr (d^(2)x)/(dt^(2)) prop -x` So motion is simple harmonic `omega = (2pi)/(T) = sqrt((4T)/(mL))rArr T = 2pisqrt((mL)/(4T))`
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