Comment on the Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Approach

摘要

An expression is developed for the energy dissipated when a constant external force is suddenly applied to the end of a particle moving in 1D subject to a conservative restoring force and a general damping force. Assuming the particle was initially at rest and ends up in static equilibrium, the fraction of the mechanical energy lost depends only on the conservative force and on the net displacement of the particle. Mechanical models are suggested to illustrate the ideas and their capacitor circuit analogies. The treatment is appropriate for an intermediate-level undergraduate mechanics course.