All bound orbits are closed under the inverse square law and in this system, which are the only two central force systems with that property, per Bertrand's theorem. An infinite number of equally spaced energy levels and eigenstate wavefunctions that are proportional to normalized Hermite functions occur in this system's (*) quantum analogue. The Q value, or quality factor, in these systems is determined by the ratio of stored energy to the energy dissipated per cycle, and varies inversely with the damping constant. The
All bound orbits are closed under the inverse square law and in this system, which are the only two central force systems with that property, per Bertrand's theorem. An infinite number of equally spaced energy levels and eigenstate wavefunctions that are proportional to normalized Hermite functions occur in this system's (*) quantum analogue. The Q value, or quality factor, in these systems is determined by the ratio of stored energy to the energy dissipated per cycle, and varies inversely with the damping constant. The equation of motion for the "simple" type of these systems can be derived from Hooke's law. For 10 points, name these systems that exhibit sinusoidal motion, exemplified by a mass on a spring.
All bound orbits are closed under the inverse square law and in this system, which are the only two central force systems with that property, per Bertrand's theorem.
harmonic oscillators [or answers with prefixes, such as "quantum", "damped", or "simple"; or linear force or Hooke's law until "energy levels" is read]