Describe the motion of a particle acted upon by a force
(i) `F= -2(x - 2)^(3)`
(ii) `F= -2(x - 2)^(2)`
(iii) `F= -2(x - 2)`

Answer

A

Explanation

(i) `F= -2(x - 2)^(3)`
`F = 0` at `x = 2`
Force is along negative x-direction for `x > 2` and it is along positive x-direction for `x < 2`.
Thus, the motion of the particle is oscillatory ( but not simple harmonic ) about `x = 2`.
(ii) `F = 0` for `x = 2`, but force is always along negative x-direction for any value of `x` except at `x = 2`. Thus, the motion of the particle is rectilinear along negetive x-direction provided it is not kept at rest at `x = 2`.
(iii) Let, us take `x - 2 = X`, then the given force can be written as,
`F = -2X`
This is the eqation of SHM. Hence, the particle oscillates simple harmonically about `X=0` or `x = 2`.