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chp36_4 - PHY2061 R D Field PHY2060 Review Simple Harmonic...

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PHY2061 R. D. Field Department of Physics chp36_4.doc University of Florida Simple Harmonic Motion Hooke’s Law Spring: For a Hooke’s Law spring the restoring force is linearly proportional to the distance from equilibrium, F x = -kx , where k is the spring constant. Since, F x = ma x we have = kx m d x dt 2 2 or d x dt k m x 2 2 0 + = , where x = x(t). General Form of 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 positive constant ( for the Hooke’s Law spring C=k/m ). The most general solution of this 2 nd order differential equation can be written in the following four ways:
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