A block on a horizontal spring obeys with

PHYSICS · Subjective · Fermi University Physics · Computational Physics · Simulating classical dynamical systems · Simulating classical dynamical systems

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

Problem

A block on a horizontal spring obeys x¨=−ω02x\ddot{x} = -\omega_0^2 x with ω0=2.0 s−1\omega_0 = 2.0\,\mathrm{s^{-1}}. At t=0t=0 it is released from x0=0.10 mx_0 = 0.10\,\mathrm{m} with v0=0 m s−1v_0 = 0\,\mathrm{m\,s^{-1}}. Using Euler-Cromer with step Δt=0.10 s\Delta t = 0.10\,\mathrm{s} (velocity updated first from the acceleration at the current position, then position updated with the new velocity): (a) Compute x1x_1 and v1v_1, the state after one step. (b) Compute x2x_2 and v2v_2, the state after a second step. (c) State how many force (acceleration) evaluations Euler-Cromer needs per step.

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