Problem $2$ Analogy between Mechanical System and Electrical System

$($a$)(26\%)$ A mass$-$damper$-$spring system is given in Figure $1.$ Use $($i$)$ the force$-$voltage

analogy and $($ii$)$ the force$-$current analogy to develop respective analogous

electrical circuits for this system. Write down the differential equations to derive

the electrical circuit. Draw the circuit diagram of the analogous circuit and denote

the parameters clearly.

$$igure $1$

$($b$)(13\%)$ An RLC circuit is given in Figure $2.$ Use the voltage$-$force analogy to

develop an analogous mechanical system for this circuit. Write down the differential

equations to derive the mechanical system. Draw the mass$-$spring$-$damper model of

the analogous mechanical system and denote the parameters clearly.