Question: d2 3. Consider the damped harmonic oscillator equation E32! + 8% (a) (8 points) Convert the above secondorder equation into a rstorder system by letting

d2 3. Consider the damped harmonic oscillator equation E32! + 8% (a) (8 points) Convert the above secondorder equation into a rstorder system by letting v = dy/dt. Show all your work and clearly state the system by presenting both differential equations together. + 153; = 0. (b) (8 points) Determine the value(s) of 3 so that the solution to the original secondorder equation is of the form y(t) = 3\". Show all your work. 4. Consider the linear system _=_ _2 dt 59 3' dy = 4. dt 3 y (a) (4 points) Rewrite the given system in matrix form. 33 (b) (8 points) Determine if the two functions Y1(t) = (g) and Y2(t) = (233) are solutions to the system of differential equations. Do this by checking to see if each function satises the system, NOT by solving the system

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