Chapter 4.1, Problem 22P

In Problems $22$ through $26$, we specift the mass, damping constant, and spring constant of an unforced spring mass system

$my\text{'}\text{'}+\gamma y\text{'}+ky=0$ (i)

Convert (i) to a planar system for the state vector $y=x_{1}i+x_{2}j\stackrel{def}{=}yi+y\text{'}j$ and use an IVP solver to:

(a) Draw Component plots of the solution of the IVP.

(b) Draw a direction field and phase portrait for the system.

(c) From the plot(s) in part (b), determine whether each critical point is asymptotically stable, stable, or unstable, and classify it as to type.

$m=1kg,\gamma =0kg/s,k=1kg/s^2,y\left(0\right)=1m,y\text{'}\left(0\right)=0m/s$(weak spring)