Points$)$ Consider the basic homogeneous spring$-$mass system, $+9+3=0,$ where y is the displacement of the mass from rest $($in meters$),$ b is the damping coefficient $($in N per m$/$sec$),$ and k is the spring constant in N$/$m$).$Let's imagine that we are modeling the sway in a small model bridge from its standard rest point. We simulat$$ anearthquake by mechanically vibrating the surface beneath the bridge. It is determined that b $=36,$ k $=72,$ m $=4.$If necessary, round all parts of your work to $2$ decimal places. $($e$.$g$.58\mathrm{.}186$ rounds to $58\mathrm{.}19)$ a$.)$ By fully showing your work and reasoning, solve this differential equation, assuming the bridge is initially stationary $($at rest$)$ and encounters an initial change in position $($velocity$)$ of $0\mathrm{.}3$ m$/$sec due to initial shock of the earthquake.b$.)$ The bridge is expected to collapse if its position from rest ever exceeds $0\mathrm{.}04$ meters. Using your solved model, determine if the bridge will collapse. If so$,$ at what time?c$.)$ Given all the same conditions, will the bridge collapse if we were to increase its mass to m $=10?$ If so$,$ at whattime? $($NOTE: you can skip a lot of the steps in part a$.$ by observing what will change in your