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 springthe restoring force is linearly proportional to the distance from equilibrium, Fx= -kx, where kis the spring constant. Since, Fx = maxwe have −=kxmd xdt22or d xdtkmx220+=, where x = x(t). General Form of SHM Differential Equation: The general for of the simple harmonic motion(SHM) differential equation is d x tdtCx t220( )( )+=, where Cis a positive constant (for the Hooke’s Law spring C=k/m). The most general solution of this 2ndorder differential equationcan be written in the following four ways:
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