For a certain oscillator the net force on the body with mass m is given by F = -cx3.

For a certain oscillator the net force on the body with mass m is given by F = -cx3.
a. What is the potential energy function for this oscillator if U=0 at x=0?
b. One-quarter of a period is the time for the body to move from x=0 to x=A. Calculate this time and hence the period.
c. According to the result of (b), does the period depend on the amplitude A of the motion? Are the oscillations simple harmonic?