An ideal inductor-capacitor circuit stores charge obeying
PHYSICS · Subjective · Fermi University Physics · Computational Physics · Electricity, Magnetism & Electromagnetism · Simulating classical dynamical systems
Computational Physics, Ch Stepping the equations of motion: four integrators measured
Problem
An ideal inductor-capacitor circuit stores charge q(t) obeying q¨=−q/(LC), with L=0.20H and C=5.0×10−4F, so the natural angular frequency is ω0=1/LC. The circuit's oscillation is integrated by plain Euler with Δt=2.0×10−4s.
(a) Without running the integration, predict the factor by which the stored energy has grown after 100 complete oscillation periods.
(b) State, without computing a new number, how the energy would behave over the same 100 periods if the circuit were instead integrated by Euler-Cromer at the same step, using the fact that Euler-Cromer's oscillator energy is known to stay bounded within a band of a few per cent, with no trend, even after 105 periods.