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chp36_5 - PHY2061 R D Field PHY2060 Review SHM Differential...

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PHY2061 R. D. Field Department of Physics chp36_5.doc University of Florida SHM Differential Equation The general for of the simple harmonic motion ( SHM ) differential equation is d x t dt Cx t 2 2 0 ( ) ( ) + = , where C is a constant. One way to solve this equation is to turn it into an algebraic equation by looking for a solution of the form x t Ae at ( ) = . Substituting this into the differential equation yields, a Ae CAe at at 2 0 + = or a C 2 = − . Case I (C > 0, oscillatory solution): For positive C , a i C i = ± = ± ω , where ω = C . In this case the most general solution of this 2 nd order differential equation can be written in the following four ways: x t Ae Be x t
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