Consider the mechanical systems given. They are all constrained to move horizontal plane. Choose the coordinates necessary first a$)$ Draw necessary free body diagrams, derive the differential equations of motion using Newtonian mechanics b$)$ Derive the differential equations of motion using Lagranges equations c$)$ Show that they are the same. d$)$ Finally put the equations in the second order matrix form e$)$ Put the system equations in vector$-$matrix form. State $=$Ax$+$Bu$,$ y$=$Cx$+$DuSolve this problem step by step and show that all solution with detail.