A particle of mass `m=3` kg is moving on a straight line in a conservative force field in which the potential energy associated with the particle is given by `U(y)=2y^(2)-30y+450`. At `t=0`, particle is at `y=8m` and moving towards positive `y`- axis with `1m//s`

Options

A. During the course of its motion the maximum speed of the particle will be `sqrt(4/3)m//s`
B. Particle will never cross the origin.
C. Particle will come to its equilibrium position for the first time at `(5pi)/(4sqrt(3))` second
D. The amplitude of oscillationi for the particle is `1m`

Answer

A, B, C, D

Explanation

`:' F=(-du)/(dy)=0` (For equiibrium)
Particle is performing simple harmonic motion