In Exercises 13-20, consider harmonic oscillators with mass m, spring constant k, and damping coefficient b. For the values specified,
(a) write the second-order differential equation and the corresponding first-order system;
(b) find the eigenvalues and eigenvectors of the linear system;
(c) classify the oscillator (as underdamped, overdamped, critically damped, or undamped) and, when appropriate, give the natural period;
(d) sketch the phase portrait of the associated linear system and include the solution curve for the given initial condition; and
(e) sketch the y(t) - and v(t) -graphs of the solution with the given initial condition.
17.
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Differential Equations
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,