Nonlinear Second Order ODE Pendulum Example

sin 0 (1) 2 2 T T K dt d where K = mgL/I O. Notice that this ODE is nonlinear (why?), but for the case of small oscillations we can make the assumption sinθ ≈θ to get the linearized equation of motion 0 (2) 2 2 T T K dt d Note that the solution to the linearized equation is given by T A sin K t B cos K t (3) • • O C θ L ................
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