$6.$ Multi DoF Problem

For the mechanical system represented by the spring$-$mass$-$damper system shown in the Figure

below write equations of motion.

Step $1.$ Setup Global Y axis

o Step $2.$ Draw the FBD of the Mass and Apply Newton$$s $2$nd law. Follow the two

conventions. Convention $1$: Set the sense of an internal force away from the mass when

it is exposed first time. Convention $2.$ To assign positive internal forces in spring and

damper choose property$*($farther displacement $$ closer displacement$)$ with respect to

the global Y axis direction.