Applications: Longitudinal oscillating chains; PDEs

[Analog_Engine.git] / scripts / TP1 10.28 Masses hanging on springs.LACE

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+# TP1 10.28 Masses hanging on springs
+# Two identical masses m are hanging on 2 springs with same spring constant D. The system is performing small oscillations around the equilibrium position.
+# m*s1'' + D*s1 + D*(s1-s2) = 0 => s1'' = D/m * (s2 - 2*s1) = D/m*s2 - D/m*s1 - D/m*s1
+# m*s2'' + D*(s2-s1) = 0        => s2'' = D/m * (s1 - s2) = D/m*s1 - D/m*s2
+
+coefficient(1): D/m_1 # D/m for s1
+coefficient(2): D/m_2 # D/m for s2, identical to D/m_1
+coefficient(3): -1 -> -s1_0 # initial position of s1
+coefficient(4): -1 -> -s2_0 # initial position of s2
+
+iintegrate D/m*s2, -D/m*s1, -D/m*s1 -> -s1' # input is s1''
+iintegrate -s1' -> s1
+   IC: -s1_0
+s1 * D/m_1 -> D/m*s1
+invert D/m*s1 -> -D/m*s1
+
+iintegrate D/m*s1, -D/m*s2 -> -s2' # input is s2''
+iintegrate -s2' -> s2
+   IC: -s2_0
+s2 * D/m_2 -> D/m*s2
+invert D/m*s2 -> -D/m*s2
+
+output(x): s1
+output(y): s2