This system will decay to a steady state most quickly when zeta equals one.
The uncertainty principle explains why one version of this system has a zero point energy of one-half h-bar times omega. This system will decay to a steady state most quickly when zeta equals one. One example of this system can be analyzed exactly using elliptic integrals, or approximately using the small-angle approximation. These systems experience unbounded growth in amplitude if driven at the resonant frequency, and their motion can be generally described using Hooke's law. For 10 points, name these systems which experience a restoring force proportional to displacement, exemplified by pendulums and springs.
The uncertainty principle explains why one version of this system has a zero point energy of one-half h-bar times omega.
simple harmonic oscillator [prompt on spring; prompt on pendulum; accept quantum harmonic oscillator until "elliptic integrals"]