Assignment:
Assume that the particle under the influence of an attractive force F(r), where r is the distance from a fixed point O, then it moves in a plane through O and the equation of motion is
(d2 u)/dθ2 +u=F(1⁄u)/(h2 u2 ),
where h is a constant, u=1⁄r and θ is the angle the line from O to the particle makes with some fixed direction in the plane.
A particle of mass 2 moves along the x-axis and is attracted towards the origin O by a force F=-8xi. If initially the particle is atx=20, and is moving to the right with speed 30 find
(a) the position of the particle at time t,
(b) the speed and the velocity of the particle at time t,
(c) the amplitude, period and frequency of the oscillations.
Provide complete and step by step solution for the question and show calculations and use formulas.