A particle of unit mass moving on the x axis has equation of motion (FUNCTION1) and the initial conditions are (FUNCTION2). show that (FUNCTION3) and deduce that the motion is an oscillation between x=1 and x=3 with period (FUNCTION4). By making the substitution (FUNCTION5) or otherwise show that (FUNCTION6).
(PLEASE SEE ATTACHMENT FOR FUNCTIONS)
I will use your "otherwise" to prove in a different, easier way!
d^x/dt^2 = -(1/3)*[2x^3 - 3x^2 - 4x + 1] = f(x)
Now the potential V(x) is given ...
This looks at teh equation of motion, initial conditions, and oscillation.