Tracking сode performance with the conservation of energy

Question

I am working with the Momentum Principle as defined by Chabay and Sherweood in their text Matter and Interactions (pf = pi+Fnet dt). The following code has been created to automate the process of updating the position and velocities of a mass on a spring in 3D. The mass is placed at the end of the spring and then the spring is pulled to its initial position r[0] and released. Since the forces involved are conservative, the total energy should be constant. My plot of the Energy is non-constant. I'm hoping someone would critique this program. Thanks

Clear[m, k, L0, r, v, p, dt, Fg, En]

m = .5;
k = 20.;
L0 = {0., .50, 0.};
r[0] = {.2, .7, -.1};
s[0] = Norm[r[0]] - Norm[L0];
Fg = m {0., -9.8, 0.};
p[0] = {0., 0., 0.};
v[0] = p[0]/m;
dt = .01;
t[0] = 0;
En[0] = .5 m v[0] . v[0] + 
  Norm[Fg] r[0][[2]] + .5 k (Norm[r[0] - Norm[L0]])^2

data = Table[
   {s = Norm[r[n]] - Norm[L0],
    p[n + 1] = p[n] + (Fg - (k s r[n])/Norm[r[n]]) dt,
    v[n + 1] = p[n + 1]/m,
    r[n + 1] = r[n] + v[n + 1] dt,
    t[n + 1] = t[n] + dt,
    En[n + 1]  = .5 m v[n + 1] . v[n + 1] + 
      Norm[Fg] r[n + 1][[2]] + .5 k s^2}, 
   {n, 0, 2000}];

ListPlot[data[[All, 6]], AxesLabel -> {"Time","Energy"}]

Answer 1

In the discussion about the momentum principle in Matter and Interactions by Chabay and Sherwood they approximate the new velocity by dividing the new momentum by the mass and then getting the new position as rf = ri + v dt. In their discussion they mention that the force is assumed to be constant over the interval dt and by taking dt smaller the resulting approximation would be better. Indeed this is the case. Here is a graph with step size decreased by 2 orders of magnitude and the number of iterations increased by 2 OOM.