Assume that the system described by the equation d'y dy +2. +ky=0 is critically damped. dt...

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Assume that the system described by the equation d'y dy +2. +ky=0 is critically damped. dt dt (a) (4 points) Give the general solution to the above equation. (b) (4 points) For the critically damped system above, assume that the initial conditions are y(0) = = 1 and -(0) dy dt = vo. If v = 0, what happens to y(t) as t o? (c) (4 points) For the critically damped system above, assume now the initial conditions y(0) = dy dt 1 and -(0) = vo for arbitrary vo. Determine a condition on vo that ensures that the mass passes through its equilibrium position at y 0 at some point after it is released. Hint: Determine all possible values of t for which y = = 0. Assume that the system described by the equation d'y dy +2. +ky=0 is critically damped. dt dt (a) (4 points) Give the general solution to the above equation. (b) (4 points) For the critically damped system above, assume that the initial conditions are y(0) = = 1 and -(0) dy dt = vo. If v = 0, what happens to y(t) as t o? (c) (4 points) For the critically damped system above, assume now the initial conditions y(0) = dy dt 1 and -(0) = vo for arbitrary vo. Determine a condition on vo that ensures that the mass passes through its equilibrium position at y 0 at some point after it is released. Hint: Determine all possible values of t for which y = = 0.

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a The general solution to the equation md2ydt2 2kdydt ky 0 for a critically damped system can be wri... View the full answer