Problem $2(25$ pts$)$

The microbridge system shown in the figure below can rotate about the $x$ axis and

translate about the $y$ axis. It is composed of a rigid central plate and two identical

flexible hinges. The hinge cross$-$section is circular with a diameter $d=2m.$ The

hinges and plate are constructed from the same material with $E=120$GPa,$G=$

$100$ GPa $,$ and $=5000k\frac{g}{m^3}.$ The thickness of the plate is $h=10m,$ and $l=$

$250m,w=200m.$

Calculate the equivalent translational spring constant along the $y$ direction.

Calculate the equivalent tortional spring constant of rotation about the $x$ axis.

Calculate the equivalent mass of the $y$ axis translation.

Calculate the equivalent mass moment of inertial of the $x$ axis rotation.