2. Consider the following harmonic oscillating system with m = 1, k = 8, b = 6, with
initial conditions y(0) = 1, and v(0) = 0.
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. Overdamped. No
natural period.
d. Identify the correct yv-phase portrait.
a.
b.
c.
d.
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5. Consider this differential equation.
a. Compute the general solution in scalar form.
b. Compute the solution in scalar form with
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