Problem $1$

A structure with rigid plate is supported by two springs. No translational motion is considered. Each

spring has a stiffness equal to $1k,k=48\mathrm{.}25l\frac{b}{i}n.$ The weight of the plate is $W=193lb.g=386i\frac{n}{s^2}.$

Write the equation of motion for the structure with the $2$ DOFs as shown in Figure $1$

Write the equation of motion for the structure with the $2$ DOFs as shown in Figure $2$

Figure $1$

Figure $2$