scripts/TP1 04.12 Harmonic Oscillator.AESL

   1 IDENTIFICATION DIVISION
   2 PROGRAM-ID HarmonicOscillator
   3 VERSION 20240201
   4 COMMENT A mass m is subject to a force F=-k*r.
   5 COMMENT What is the trajectory if the mass starts at position (a,0,0)?
   6 COMMENT How much time does it take to pass through zero?
   7 COMMENT What is the trajectory if it starts at (a,0,0) with velocity (0,v0,0)?
   8 COMMENT m*x'' = -k*x
   9 COMMENT m*y'' = -k*y (z can be set to 0).
  10
  11 ENVIRONMENT DIVISION
  12 ENGINE Anabrid-THAT
  13 TIMEBASE 1ms
  14 REQUIRES COEFFICIENT 4, INTEGRATOR 4, INVERTER 2
  15
  16 DATA DIVISION
  17 OUTPUT OUTPUT.X x
  18 OUTPUT OUTPUT.Y y
  19 COEFFICIENT.1 A     # (a,0,0)
  20 COEFFICIENT.2 K/M_x # k/m for x
  21 COEFFICIENT.3 V0    # (0,v0,0)
  22 COEFFICIENT.4 K/M_y # k/m for y, identical to k/m for x
  23
  24 PROGRAM DIVISION
  25 -1 -> COEFFICIENT.A -> -a # has to be negative because x' is negative
  26 +1 -> COEFFICIENT.V0 -> v0 # has to be positive because y'' is positive
  27
  28 x'' -> INTEGRATOR -> -x'
  29 -x', IC:-a -> INTEGRATOR -> x
  30 x -> COEFFICIENT.K/M_x -> k/m*x
  31 k/m*x -> INVERTER -> -k/m*x = x''
  32
  33 y'', IC:v0 -> INTEGRATOR -> -y'
  34 -y' -> INTEGRATOR -> y
  35 y -> COEFFICIENT.K/M_y -> k/m*y
  36 k/m*y -> INVERTER -> -k/m*y = y''
  37
  38 OPERATION DIVISION
  39 MODE REPEAT
  40 OP-TIME 100 ms