‫بسم هللا الرحمن الرحيم‬
Coupled Oscillations
Zain Yamani
Saudi Physical Society
Rabi-I, 1433
Agenda for Lecture-6:
1.
2.
3.
4.
Administration..
Two coupled oscillations
General theory of oscillations
A few comments about the homework
Administration
What I have posted on the course web-site
Make sure the TAs are happy with you!  stick to your
commitments (lessons, interactiONs)
Let me know how we can make the Course better..
Try to listen/ study the Playback to instill the lessons
learnt in your minds/ psyche
The next class is this Saturday (not Sunday!)
See how simple Mathematica makes it seem to be!!
(interacion-3.b in one line )
Also check: under-damped harmonic oscillator
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..
• Two masses connected to opposite walls with (weak/ strong) coupling
• The special case when the coupling is ineffective (through special initial conditions)
Check the mathematica program after deriving the problem. Play with initial
conditions. Note how the energy transfers from one oscillator to the other. (the
exception is when we start in a pure mode (either pure mode-1 [alone] OR mode-2
[alone].
Oscillations..
• The general case of “n” masses in 3-D.. (3n – 6)  in linear: (3n-5)
T, V
See note..
Non-degenerate, first 
What do we intend to do next Session?!!