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Unformatted text preview: Group Project MAP 2302 In this project, we’ll re-examine mass-spring systems to validate a hunch from the first project, and to discuss the idea of a resonant frequency. Recall that the second-order equation involving the spring equation is: ( * ) mx 00 + bx + kx = f ( t ) where m,b,k are nonnegative constants representing the mass, friction coefficient, and spring con- stant, and f ( t ) is any other external force on the spring that varies with time. 1. Suppose the spring shown in the figure at right, is stretched a distance A from its equilibrium position, and then released. We assume there are no external forces. (a) Divide by m to rewrite the equation ( * ) with new constants λ = b m and μ = k m . Then, write the general solution to this homogeneous equation in the case that λ 2 > 4 μ , and in the case that λ 2 < 4 μ (we will ignore the case that they are equal). (b) Explain with limits, why, in every case, the solution representing the motion of the spring with tend to zero with time. In one of the two cases, one ofwith tend to zero with time....
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- Spring '08