A particle P of mass m=1 moves on the x-axis under the force field

Question

F=36/(x^3) - 9/(x^2) (x>0).

Show that each motion of P consists of either (i) a periodic oscillation between two extreme points, or (ii) an unbounded motion with one extreme point, depending on the value of the total energy.

Regards

Answer 1

This is a very old problem.

you know force= mass*acceleration

so start with the force, and find displacement as a function of time.
I will get you started.

F=ma=36/x^3 -9/x^2

but a= f" where x" is the second derivative of position with respect to time
See if you can get to f.