Question

[1] (a) Obtain the transfer function of the spring-mass-dashpot system mounted on a cart. Let u(t) be the input to the system, and y(t) is the output. Find the Force-Volt and Force-current analogy. Massless cart TII

Answer 1

mk fm fb The given mechanical system has one node (mass). Displacement of mass m is y, and the corresponding velocity be v The free body diagram of mass im į represented at The applied input force is ut) 7 ult) and the remaining forces are opposing forces on mass. write the force balance equation ult) = fm + fb + fk 41+) = m. art + become + k.= 0 geplace the displacement by velocity. alt)= m. art + bv + k Svidt L® Leden av Apply Laplace transform to equation & Suidt U(s) = m. $ 415) + bo S. Yls) +*+Y/s) UIB)- 469)[m$+bs+k] Tommas fet motos tk

Force - voltage analogy.'- The force applied to mass 'm' is represented by Voltage source. The mechanical system has one node (mass) hence the borce- voltage analogy Electrical circuit has one mesh. The Electrical analogous Elements for the elements of mechanical system are, - ult) elt) mL byr kt velocity, vy l → The tolle -voltage selectrical analogous cismit is avrova elt) Apply kischoff's voltage low, elt) = iR+ Lichid +Sialt): The above equation is similar to the differential equation in ②. Forle - current analogy'a face applied to mass mi is applied (represented I as a cusrent source in the circuit. - The given mechanical system has one mass. hence. the analogous Electrical ciemit has one node. an

Elements of - the electrical analogous Elements for the mechanical systein are, Ult) iH), m+c, b + , K → velocity, V v itt) @ Rest L Apply kischoff's current law at node. coat + ☆ + . SV.at = ilt) which is similar to the mechanical system differential equation in equation ② . Me