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1 # TP1 10.30 Linear Molecule
2 # In a linear molecule of symmetric construction of type A-B-A the atoms are harmonically coupled and are performing small oscillations around the equilibrium positions.
3
4 # s1'' = -omega0^2*s1 + omega0^2*s2
5 # s2'' = -my (-omega0^2*s1 + omega0^2*s2 + omega0^2*s2 - omega0^2*s3)
6 # s3'' = omega0^2*s2 - omega0^2*s3
7
8 # NB: all integrators have to run with 100 nF capacitance, i.e. SLOW mode
9
10 coefficient(1): omega0^2_1 # omega0^2 for s1
11 coefficient(2): omega0^2_2 # omega0^2 for s2 # same as omega0^2_1
12 coefficient(3): omega0^2_3 # omega0^2 for s3 # same as omega0^2_1
13 coefficient(4): my
14 coefficient(5): -1 -> -s1_0 # initial position of s1
15 coefficient(6): -1 -> -s3_0 # initial position of s3
16 # initial positon of s2, the central mass, is set to 0
17
18 iintegrate -omega0^2_1*s1, omega0^2_2*s2 -> -s1' # input is s1''
19 iintegrate -s1' -> s1
20 IC: -s1_0
21 invert s1 -> -s1
22 -s1 * omega0^2_1 -> -omega0^2_1*s1
23
24 iintegrate -my*bracket -> -s2' # input is s2''
25 # the following integrator has to be built up manually as THAT only has 5 integrators and we need 6
26 # iintegrate -s2' -> s2
27 openamp -s2' -> s2
28 loopback: capacitor(100nF)
29 s2 * omega0^2_2 -> omega0^2_2*s2
30 isum -omega0^2_1*s1, omega0^2_2*s2, omega0^2_2*s2, -omega0^2_3*s3 -> -bracket
31 -bracket * my -> -my*bracket
32
33 iintegrate omega0^2_2*s2, -omega0^2_3*s3 -> -s3' # input is s3''
34 iintegrate -s3' -> s3
35 IC: -s3_0
36 invert s3 -> -s3
37 -s3 * omega0^2_3 -> -omega0^2_3*s3
38
39 output(x): s1
40 output(y): s2
41 output(z): s3