The position of a certain spring-mass system satisfies t
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The position of a certain spring-mass system satisfies the initial value problem y?? + 1 4 y? + 2y = 0, y(0) = 0, y? (0)
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The position of a certain spring-mass system satisfies the initial value problem y?? + 1 4 y? + 2y = 0, y(0) = 0, y? (0) = 2. (a) Find the solution of this initial value problem. (b) Plot y versus t and y? versus t on the same axes. (c) Draw the phase portrait for the dynamical system equivalent to y?? + 1 4 y? + 2y = 0. Include the trajectory corresponding to the initial conditions y(0) = 0, y? (0) = 2.
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