The displacement `x` of a particle in motion is given in terms of time by `x(x-4) =1 -5 cos omegat`

Options

A. the particle executes SHM
B. the particle executes oscillatory motion which is not SHM
C. the motion of the particle is neither oscillatory nor simple harmonic
D. the particle is not acted upon by a force when it is at x = 4

Answer

A

Explanation

`x^(2) - 4x = 1 - 5 cos omega t`
`x^(2) - 4x + 4 = 5 - 5 cos omega t`
`(x - 2)^(2) = "10 sin"^(2) (omega t)/(2)`
`x - 2 = sqrt(10) "sin" (omega t)/(2)`
it is an SHM with `A = sqrt(10)` and angular frequency `(omega)/(2)`