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Consider the initial value problem my?? + ?y? + ky = 0,

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Consider the initial value problem my?? + ?y? + ky = 0, y(0) = y0, y? (0) = ?0. Assume that ?2 < 4km. (a) Solve the init

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Consider the initial value problem my?? + ?y? + ky = 0, y(0) = y0, y? (0) = ?0. Assume that ?2 < 4km. (a) Solve the initial value problem. (b) Write the solution in the form y(t) = R exp(??t?2m) cos(?t ? ?). Determine R in terms of m, ?, k, y0, and ?0. (c) Investigate the dependence of R on the damping coefficient ? for fixed values of the other parameters.

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