A very very very simple velocity-Verlet algorithm for a particle under harmonic potential

index.js

var k, m, pos0, vel0, PREC;

PREC = 1e-5; // tolerance for float num

k = 1.0; // potential(x) = k * x^2 / 2
m = 1.0; // mass
pos0 = 1.0; // init condition pos(0)
vel0 = 1.0; // init condition vel(0)

var equalZero = function(n) {
  if (n === 0 || ((n < PREC) && (n > -PREC))) return true;
  else return false;
}

var force = function(t, dt) {
  console.log(`force(${t}, ${dt})`);
  return k*pos(t - dt, dt);
}

var pos = function(t, dt) {
  console.log(`pos(${t}, ${dt})`);
  if(equalZero(t)) return pos0;
  else return pos(t - dt, dt) + vel(t - dt, dt)*dt + force(t, dt) / (2 * m) * dt * dt;
}

var vel = function(t, dt) {
  console.log(`vel(${t}, ${dt})`);
  if(equalZero(t)) return vel0;
  else return vel(t - dt, dt) + dt / (2 * m) * (force(t, dt) + force(t + dt, dt));
}

q = [
  pos(0.1, 0.1),
  vel(0.1, 0.1),
  pos(0.2, 0.1),
  vel(0.2, 0.1),
];

console.log(q); // [ 1.105, 1.10525, 1.22105, 1.2215525 ]