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__________

Answer

2

Explanation

`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`