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بسم الله الرحمن الرحيم. Coupled Oscillations Zain Yamani Saudi Physical Society Rabi-I, 1433. Agenda for Lecture-7:. Administration.. General theory of oscillations Double-pendulum CO 2 molecule oscillations A few comments about the homework. Administration.
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بسم الله الرحمن الرحيم Coupled Oscillations Zain Yamani Saudi Physical Society Rabi-I, 1433 Agenda for Lecture-7: Administration.. General theory of oscillations Double-pendulum CO2 molecule oscillations A few comments about the homework
Administration What I have posted on the course web-site As a next interaction, I want you to help me beef up the “Relevant Web-sites” section of my course page. We are approaching the end..
Oscillations.. • SHO (at mass connected with a spring to a rigid wall) • Connecting the mass to more than one spring (parallel/ series) • Simple pendulum • Harmonic Oscillator for two (same or different) masses connected with a spring • Two masses connected to opposite walls without coupling • Two masses connected to opposite walls with (weak/ strong) coupling • The special case when the coupling is ineffective (through special initial conditions) • The general case of “n” masses in 3-D.. (3n – 6) in linear: (3n-5) • Two pendula hanging from one another esp. the special case when they act as one swinging pendulum (through special initial conditions) • Three masses (as in CO2 molecule) • The role of symmetry and the importance of Group Theory • Coupled oscillator (two dipoles) as in solid state physics and the 6-12 potential
Oscillations.. • The general case of “n” masses in 3-D.. (3n – 6) in linear: (3n-5) T, V: what are the Ajk and mjk? See notes.. Non-degenerate, first two coupled oscillators.nb Check the weak coupling case Play with the code, at home..
Double Pendulum • Two pendula hanging from one another esp. the special case when they act as one swinging pendulum (through special initial conditions ) Note that the T-1 M is not orthogonal Do you remember the four masses connected with springs on the rim of a circle??! Oh.. Oh!!!! we have degeneracy! Let’s take a step back to mathematics (linear algebra) and see how we deal with degeneracy.
Oscillations.. • Three masses (as in CO2 molecule) • The general case of “n” masses in 3-D. • 3 Translation, 3 (or 2??) rotation and the rest [(3n – 6) in linear: (3n-5)] vibration modes • Let’s concentrate on longitudinal modes!! • What about the transverse modes?
