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 tdtCx t220( )( )+=, where Cis a constant. One way to solve this equation is to turn it into an algebraic equationby looking for a solution of the form x tAeat( )=. Substituting this into the differential equation yields, a AeCAeatat20+=or aC2= −. Case I (C > 0, oscillatory solution): For positive C, aiCi= ±= ±ω, where ω=C. In this case the most general solution of this 2ndorder differential equationcan be written in the following four ways: x tAeBex t
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