An object of mass `m` is attached to a spring. The restroing force of the spring is `F - lambdax^(3)`, where `x` is the displacement. The oscillation period depends on the mass, `l`mabd and oscillation amplitude. Suppose the object is initially at rest. If the initial displacement is `D` then its period is `tau`. If the initial displacement is `2D`, find the period.

Options

A. `8tau`
B. `2tau`
C. `tau`
D. `tau//2`

Answer

D

Explanation

Through dimensional analysis `[lambda] = [ML^(-2)T^(-2)]`
`T prop m^(a)lambda^(b)A^(c)`
`[T] = [M]^(a) [ML^(-2)T^(-2)]^(b)[L]^(c)`
`a = 1/2, b = (-1)/(2), c = -1`
`T = prop (1)/(A)`