A spring hanging straight down from the ceiling with a weight attached to the end can be modeled by exactly the same ODE as a pendulum [which we looked at earlier in the class). If we attach a second spring to the weight of the rst spring, then we can model the whole thing as a system of two second-order CIDEs. For example, with some oonvenient values chosen for the masses and spring constants, we get the system $+5x=2y d23- _ Here, 3 represents the distanee that the upper spring is stretched from its natural length and 3,; represents the distance that the lower spring is stretched from its natural length. {A positive value of a: or y means that the mass is farther from the ceiling, while a negative value means that the mass is closer to the eeiling.) l. Rewrite this system as a system of four rst-order ODEs. You should get an ODE of the form 1: = Ax, where Aisar-lxdmatrix