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Unformatted text preview: Notes for Day : § . : Forced Mechanica Vibrations In section § . , we talked about the action of a weight on a spring, which we modeled with the equation: my ′′ + γy ′ + ky = (Recall the middle term is “gamma y prime”; the gamma and the y look very similar.) In this model, the oscillations of the spring were induced solely by the initial conditions on the system: the weight on the spring is pulled away and released, for example. If there is an external force acting on the weight over time, we say that the system exhibits forced vibration . e mathematical model for a system exhibiting forced vibration is my ′′ + γy ′ + ky = g ( t ) , the nonhomogeneous version of the equation from section § . . Section § . describes forced vibrations in detail, but we’re going to restrict our attention to four simple cases: Case : y ′′ + ky = F cos ( ωt ) or y ′′ + ky = F sin ( ωt ) ....
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 Spring '06
 EDeSturler
 Equations, Characteristic polynomial, Complex number, di erential equation

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