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بسم هللا الرحمن الرحيم Coupled Oscillations Zain Yamani Saudi Physical Society Rabi-I, 1433 Agenda for Lecture-5: 1. 2. 3. 4. Administration.. A few more remarks on diagonalization Intro. Lagrangian Mechanics Oscillations.. Administration I hope you have started reading M&T.. [I assume you all have the book. Right?] I will soon (also) pass out hand-outs 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 class next Sunday I need to change it to Saturday What’s special today? We will start to oscillate.. Every time I say: what do you think, I like to see better than 80% response!! A few quizzes/ questions which you will enjoy A few more remarks on diagonalization - Check inverse and diagonal with Mathematica - When we see a matrix representation, what is coupled and what is decoupled? - Same representation.. Different operators?? -Removing degeneracy through perturbation.. - A to the ten!! Intro. to Lagrangian Mechanics What is Lagrangian Mechanics? Why Lagrangian? Lagrangian in one and more dimensions - free fall - down an incline - projectile motion in 2-d - simple 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) • 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 general case of “n” masses in 3-D.. (3n – 6) in linear: (3n-5) •The role of symmetry and the importance of Group Theory • Coupled oscillator (two dipoles) as in solid state physics and the 6-12 potential What do we intend to do next Session?!!