Further examples of harmonic oscillation

[Analog_Engine.git] / scripts / EP1 10.02 Forced Harmonic Oscillator.LACE

# Forced Damped_Harmonic Oscillator
# x'' + 2*delta*x' + omega.0^2*x = A cos (omega.f t)

# generating oscillation with omega.f
# f'' = -omega.f^2*f
coefficient.1(-1) -> -f0      # amplitude
coefficient.2     -> omega^2
iintegrate f'' -> -f'
iintegrate -f' -> f
  IC: -f0
cmultiply f, omega^2 -> omega^2*f
invert omega^2*f -> -omega^2*f
assign -omega^2*f -> f''
invert f -> -f
output f -> y

# forced damped harmonic oscillation
# x'' = -(2*delta*x' + omega.0^2*x) + A cos (omega.f t)
coefficient.5(-1) -> -x0       # amplitude of oscillation
coefficient.6     -> 2*delta   # attenuation
coefficient.7     -> omega.0^2 # Eigenfrequency of this oscillator, ^2

iintegrate x'' -> -x'
invert -x' -> x'
cmultiply x', 2*delta -> 2*delta*x'

iintegrate -x' -> x
  IC: -x0
cmultiply x, omega.0^2 -> omega.0^2*x
isum 2*delta*x', omega.0^2*x, -f -> -(2*delta*x'+omega.0^2*x)-f
assign -(2*delta*x'+omega.0^2*x)-f -> x''

output(x) -> x