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

Particle will come to its equilibrium position for the first time at  $\frac{5\pi }{4\sqrt{3}}$ second

The amplitude of oscillation for the particle is 1m  

During the course of its motion the maximum speed of the particle will be $\sqrt{\frac{4}{3}}\text{m/s}$

Particle will never cross the origin