scripts/EP1 10.02 Forced Harmonic Oscillator.LACE

   1 # Forced Damped_Harmonic Oscillator
   2 # x'' + 2*delta*x' + omega.0^2*x = A cos (omega.f t)
   3
   4 # generating oscillation with omega.f
   5 # f'' = -omega.f^2*f
   6 coefficient.1(-1) -> -f0      # amplitude
   7 coefficient.2     -> omega^2
   8 iintegrate f'' -> -f'
   9 iintegrate -f' -> f
  10   IC: -f0
  11 cmultiply f, omega^2 -> omega^2*f
  12 invert omega^2*f -> -omega^2*f
  13 assign -omega^2*f -> f''
  14 invert f -> -f
  15 output f -> y
  16
  17 # forced damped harmonic oscillation
  18 # x'' = -(2*delta*x' + omega.0^2*x) + A cos (omega.f t)
  19 coefficient.5(-1) -> -x0       # amplitude of oscillation
  20 coefficient.6     -> 2*delta   # attenuation
  21 coefficient.7     -> omega.0^2 # Eigenfrequency of this oscillator, ^2
  22
  23 iintegrate x'' -> -x'
  24 invert -x' -> x'
  25 cmultiply x', 2*delta -> 2*delta*x'
  26
  27 iintegrate -x' -> x
  28   IC: -x0
  29 cmultiply x, omega.0^2 -> omega.0^2*x
  30 isum 2*delta*x', omega.0^2*x, -f -> -(2*delta*x'+omega.0^2*x)-f
  31 assign -(2*delta*x'+omega.0^2*x)-f -> x''
  32
  33 output(x) -> x