a rope slides frictionlessly down the edge of a table

[Analog_Engine.git] / scripts / TP1 04.12 Harmonic Oscillator.AESL

IDENTIFICATION DIVISION
PROGRAM-ID HarmonicOscillator
VERSION 20240201
COMMENT A mass m is subject to a force F=-k*r.
COMMENT What is the trajectory if the mass starts at position (a,0,0)?
COMMENT How much time does it take to pass through zero?
COMMENT What is the trajectory if it starts at (a,0,0) with velocity (0,v0,0)?
COMMENT m*x'' = -k*x
COMMENT m*y'' = -k*y (z can be set to 0).

ENVIRONMENT DIVISION
ENGINE Anabrid-THAT
TIMEBASE 1ms
REQUIRES COEFFICIENT 4, INTEGRATOR 4, INVERTER 2

DATA DIVISION
OUTPUT OUTPUT.X x
OUTPUT OUTPUT.Y y
COEFFICIENT.1 A     # (a,0,0)
COEFFICIENT.2 K/M_x # k/m for x
COEFFICIENT.3 V0    # (0,v0,0)
COEFFICIENT.4 K/M_y # k/m for y, identical to k/m for x

PROGRAM DIVISION
-1 -> COEFFICIENT.A -> -a # has to be negative because x' is negative
+1 -> COEFFICIENT.V0 -> v0 # has to be positive because y'' is positive

x'' -> INTEGRATOR -> -x'
-x', IC:-a -> INTEGRATOR -> x
x -> COEFFICIENT.K/M_x -> k/m*x
k/m*x -> INVERTER -> -k/m*x = x''

y'', IC:v0 -> INTEGRATOR -> -y'
-y' -> INTEGRATOR -> y
y -> COEFFICIENT.K/M_y -> k/m*y
k/m*y -> INVERTER -> -k/m*y = y''

OPERATION DIVISION
MODE REPEAT
OP-TIME 100 ms