Further examples of harmonic oscillation

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

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+# 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