Consider a three dimensional harmonic oscillator with a nonlinear force such that the potential

a) calculate the force.
b) what is the lagrangian for this system?
c) what are the euler-lagrange equations?
d) find the effective potential.
e) what kind of orbits are possible-consider both small angular momentum and large angular momentum.
f) when they exist, find the radii of possible circular orbits as a function of the angular momentum.
g) which, if any of these orbits are stable?
h) for stable orbits, what is the frequency of small oscillations.

Answertraveling around a circular trackexplanation"traveling around a circular track" is the best answer as you could be traveling around a circular track at a constant speed. your velocity would therefore have the same magnitude but will always be constantly direction. since acceleration is the rate of change of velocity, the rate of change will only involve the direction of velocity and not the magnitude.wrong choices: "an object at rest" does not accelerate at all"increasing speed while traveling around a curve" means that the acceleration will not be constant due to only change in direction; it will be constant due to both magnitude and direction"an object in free fall" does not necessarily change direction 

Ibelieve the answer is d. macula  hope my answer has you : )

Ithink the answer is c. make unnecessarily  wide gestures