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An elastic string of unit cross-sectional area and natural length (a+b) where a gt b and modulii of elasticity Y has a particle of mass m attached to it at a distance a from one end, which is fixed to a point A of a smooth horizontal plane. The other end of the string is fixed to a point B. so that string is just unstretched. If particle is diplacement towards right by. distance x_(0) and then released then |
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Answer» The TIME period of the oscillation will be `PI(sqrt(a)+sqrt(b))sqrt((m)/(Y))`  from `t_(B RARR 0)` `T = y (X)/(a) rArr (d^(2)x)/(dt^(2)) = (-y)/(am) x rArr t_(B rarr 0) = (pi)/(2) sqrt((am)/(y))` simply `t_(B rarr 0)` other ext. `= (pi)/(2) sqrt((bm)/(y))` Time period `= pi = sqrt((m)/(y)) (sqrta + sqrtb)` `(y x_(0)^(2))/(2a) = (yc^(2))/(2b)` `c = x_(0) sqrt((b)/(a))` Distance (ext to ext) `x_(0) + c = x_(0) ((sqrtb + sqrta))/(sqrta)` |
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