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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
10coefficient(1): omega0^2_1 # omega0^2 for s1
11coefficient(2): omega0^2_2 # omega0^2 for s2 # same as omega0^2_1
12coefficient(3): omega0^2_3 # omega0^2 for s3 # same as omega0^2_1
13coefficient(4): my
14coefficient(5): -1 -> -s1_0 # initial position of s1
15coefficient(6): -1 -> -s3_0 # initial position of s3
16# initial positon of s2, the central mass, is set to 0
17
18iintegrate -omega0^2_1*s1, omega0^2_2*s2 -> -s1' # input is s1''
19iintegrate -s1' -> s1
20 IC: -s1_0
21invert s1 -> -s1
22-s1 * omega0^2_1 -> -omega0^2_1*s1
23
24iintegrate -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
27openamp -s2' -> s2
28 loopback: capacitor(100nF)
29s2 * omega0^2_2 -> omega0^2_2*s2
30isum -omega0^2_1*s1, omega0^2_2*s2, omega0^2_2*s2, -omega0^2_3*s3 -> -bracket
31-bracket * my -> -my*bracket
32
33iintegrate omega0^2_2*s2, -omega0^2_3*s3 -> -s3' # input is s3''
34iintegrate -s3' -> s3
35 IC: -s3_0
36invert s3 -> -s3
37-s3 * omega0^2_3 -> -omega0^2_3*s3
38
39 output(x): s1
40 output(y): s2
41 output(z): s3