(Solved): Consider a three-DOF system shown below. Figure 3: A 3DOF spring-mass-damper system a) Find the equ ...

Consider a three-DOF system shown below. Figure 3: A 3DOF spring-mass-damper system a) Find the equation of motion using Newton's \( 2^{\text {nd }} \) Law. Show your work. Express this equation in that canonical matrix form \( M \ddot{\vec{q}}+C \dot{\vec{q}}+K \vec{q}=\vec{F} \).