Find the eigenvalues, determine if the origin is a spiral sink, a spiral source, or center

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(a) Find the eigenvalues;
(b) determine if the origin is a spiral sink, a spiral source, or a center;
(c) determine the natural period and natural frequency of the oscillations,
(d) determine the direction of the oscillations in the phase plane (do the solutions go clockwise or counterclockwise around the origin?)

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