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.

stands for electromotive force and it is measured in volts. despite its name, it is not actually the force in the sense of being a "pushing" or "pulling" (not measured in newtons).an equation that relates emf,  ℰ,  to a battery's terminal voltage, v, current, i, and internal resistance, r, is    ℰ = v + irin this case, the emf can be interpreted as a voltage—a difference in electric potential.i would not say that it would be considered an energy. if emf can be defined as the energy/work per a unit charge from a battery or other electric source, then it is not strictly energy.

Isso9