Question

Determine an equivalent electrical circuit using a voltage source and passive elements such as resistors, inductors, and capacitors that collectively have a similar ODE to the mechanical system shown below. Steps:

a) Derive the non-homogeneous ODE of the forced mechanical vibrating system

b) Arrange electrical components into an equivalent circuit with the aid of textbook Table 6-1.

c) Derive the circuit ODE to demonstrate similar structure to the ODE of part a)

d) Repeat parts b and c as needed to arrive at a matching structure. [ use in-class example and textbook’s “Example Problems and Solutions” which are similar to guide you].

f(t) C1 C2 k3 m1 m2 k1 k2

Answer 1

(76 fit MI + "f + 2 = 8 + K Cdxx) 2 + k2(x,-2x ,) + d 77 P o

C d x ー ズ)+K,(ーメ,) 2- +K32 Mee Veloc:ty V - d2x dv dヒ dx dt / =7)f +K,C Jvi-v) +M A P M dV2 +9Cv-4) (Jv-v,) V2-V 2- FAP + J2 O

2

ER 1 Electrical system (node basis system) TABLE 5 Mechanical system Item Current, i Force, f Independent variable (input) Voltage, V Velocity, V Dependent variable Flux, Displacement, x (output) Conductance G 1/R Frictional coefficient Dissipative element of dashpot, B Storage element Mass, M Capacitance, C Stiffness of spring, K Inverse of inductance, 1/L Physical law Newton's second law Kirchoff's current law

fltelt Vii M,=L M2 L2 CK3 L2 uer RL +- C2 elヒ) Force Vol bage anal