Question $6$

a$)$ The spring mass damper system illustrated in Fig.Q$6$a is well suited for modelling objects with complex material properties such as nonlinearity and viscoelasticity.

Fig.Q$6$a: Spring mass damper system

i$.$ Draw the free$-$body diagrams for each mass.$[4]$

ii$.$ Determine the differential equations describing the system. $[6]$

iii. Deduce the transfer function of the system. $[8]$