PHY354H1 Lecture Notes - The Roots, Scion Tc, Identity Matrix
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Lecture 16: coupled oscillators & normal modes: relevant reading: morin 4. 5, reminder: november break next monday & tuesday, so no tutorial next week. Ta"s will have o ce hours during their wednesday tutorial times. Finding the natural frequencies or normal modes : last time we derived the following equation for the coupled pendulums" motions: d2xa dt2 + d2xb dt2 + In fact, i recommend trying the derivation to the equations below using these other forms yourself: these natural frequencies are called normal modes of the sys- tem. 0b 2 c (a b) = 0 c (a b) = 0 (1) (2) If we can nd an that satis es these equations, then we have found states of the system where all the components oscillate with the same frequency. We said there were 2 ways to solve these equations. Last time we did the substitution" method to nd two natural (or normal mode) frequencies: