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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 dxt 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 xt Ae at = . Substituting this into the differential equation yields, aA e CA e 2 0 or aC 2 =− . Case I (C > 0, oscillatory solution): For positive C , ai Ci =± ω , where = 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 Be A t B t A t A t it co
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