A mass on a frictionless horizontal spring has natural angular frequency and is…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Computational Physics · Simulating classical dynamical systems

Computational Physics, Ch Stepping the equations of motion: four integrators measured

Problem

A mass on a frictionless horizontal spring has natural angular frequency

\omega_0 = 2.0\,\mathrm{s^{-1}}

and is integrated by plain Euler with

\Delta t = 0.02\,\mathrm{s}

. Without running the integration, use the exact one-step energy multiplication factor for Euler on the harmonic oscillator,

E_{n+1} = (1+\omega_0^2\Delta t^2)E_n

, to predict the factor by which the mechanical energy has grown after

5

complete periods. State whether this drift is bounded or growing, and give its sign.