' ftablib.bas - jackord@kw.igs.net - revised 18 Mar 04 - Liberty Basic v4.00
' Euler and Feynman tables for the motion of a mass attached to a spring.
' The mass is initially passing through the equilibrium position at 2.8 m/s,
' and the motion is followed for 1 s at 1/n s intervals.
' The Euler Algorithm uses:     y(t + dt) = y(t) + v(t) * dt
'                               v(t + dt) = v(t) + a(t) * dt
' The Feynman Algorithm uses:   y(t + dt) = y(t) + v(t + dt/2) * dt
'                               v(t + dt/2) = v(t - dt/2) + a(t) * dt
  k=8: m=2: n=5: dt=.2

  print "Euler Algorithm": print
  print "Time", "Position", "Velocity", "Acceleration"
  t=0: y=0: v=2.8: a= 0-k*y/m
  print t, y, v, a
  for i = 1 TO n
    t=t+dt: y=y+v*dt: v=v+a*dt: a=0-k*y/m
    print t, y, v, a
  next i

  print: print: print "Feynman Algorithm": print
  print "Time", "Position", "Velocity", "Acceleration"
  t=0: y=0: v=2.8: a=0-k*y/m
  print t, y, v, a
  v=v+a*dt/2
  for i=1 TO n
    t=t+dt: y=y+v*dt: a=0-k*y/m
    print , , v: print t, y, , a
    v=v+a*dt
  next i
  end