InterviewSolution
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InterviewSolution
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A particle of mass `1kg` constrained to move along x axis under the action of the only conservation force for which the potential energy is given by `u = x^(3) - 4x^(2)` and was initially at rest at stabel equilibrium position and was very slightly displaced along x axis and then it oscillates with a period of `(pi)/(sqrt(x))`sec, the value of x is__________ |
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Answer» Correct Answer - 2 `u = x^(3) - 4x^(2)` `F = 8x - 3x^(2)` So, `x = 0, x = (8)/(3)` are equilibrium `(dF)/(dx) = (8-6x)` so at `x = (8)/(3) (dF)/(dx) =- ve` `rArr x = (8)/(3)` is stable equilibrium `dF =- (8) dx` `(dF)/((1)) =- ((8))/((1))dx` `a =- 8dx` So `omega = sqrt(8) T = (2pi)/(sqrt(8)) = (pi)/(sqrt(2))sec` |
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