Consider a harmonic oscillator with mass m=1 , spring constant k=7, & damping coefficient b=8

A.) write the second order differential equations and corresponding first order system

B.) find the eigenvalues and Eigenvectors of the system

C.) find the general solution

D.) find the solution that satisfies the initial conditions y(0)=-1 , v(0)=5

E.) sketch the solution curve (question d) in the (y,v) plane

F.) sketch the y(t) and v(t) graphs o the solution of the initial value problem

I have include some photos of my work, I'm pretty confident about all the parts except e & f