Problem$-1$: A square rod of length $L$ is attached to an unyielding support through a frictionless

hinge connection at one end. The rod is rigidly attached to two identical thin circular disks. one

at the free end and other at the mid$-$span. Cross$-$sectional dimension of the rod is $dxd$ : diameter

of the disk is $D$; and thickness of the disk is $t_{h.}.$ Assume the rod and the disk are made of the

same material with mass density $$ and Young's modulus as infinity $($Rigid$).$ The rod is

supported through a spring of stiffness coefficient $K$ and a dashpot of pure viscus damping

coefficient $C.$ as shown in Figure $1.$

A weight W is released from a height $H($as shown$)$ and that gets attached to the rod surface

without bouncing and sliding after the impact. Derive $/$ find out the followings:

a$)$ Equation of the motion of the system

b$)$ Natural frequency

c$)$ Damping ratio

If the disks are approximated as point masses neglecting the finite dimension, estimate the natural

frequency and damping ratio.