Parallel resonance

摘要

A child sits on a swing, feet dangling, perfectly at rest. Give him a gentle push. The child moves forward to a maximum height, reverses course under the influence of gravity, and then swings back and forth. The height of the child's excursions depends on the energy, E_1, supplied by your initial push. Damping forces, such as air resistance and the child's foot-dragging, rob energy from each cycle. These damping forces control the ride's duration but have little to do with the size of the initial excursion. Mathematicians define the damping constant, Q, as the ratio of energy stored within the system divided by energy lost per radian of oscillation. The higher the damping constant is, the lower the rate of energy loss, and the longer the ride.