helpQ$2$ An anti$-$vibration system for a very sensitive machinery equipment is modelled as a

mass$-$spring$-$damper system given in Figure Q$2\mathrm{.}1$ consists of two mass blocks $M_1$ and

$M_2.$ The stiffness for first spring and second spring are $K_1$ and $K_2$ respectively. The

damper connecting the mass blocks has the damping coefficient $C.$ Assume the first

mass block is on the frictionless surface while the second mass block has the surface

friction coefficient of $B.$ Consider the input is the displacement given to the first spring,

$x_1$ while the output is the displacement of the second mass, $x_3.$ Derive all equations

related to this system and construct the system's block diagram.

$(15$ marks$)$

Figure Q$2\mathrm{.}1$