Question

3. Derive complete analogy between series RLC circuit and rotational mechanical system parameterized by b, J, k 4. Use MATLAB/Simulink to calculate Eigen values /Eigen Vectors of A= 1 -1 2 0 1 0 3 2 1

Answer 1

From the Question - 3 Analogy between R Le circuit and Rotational Mechanical system. Consider the cleemical System . R m + V mesh Analysis de at Acconding to VE Ri + L de ce te fidt Alice Lease) * = ( dt de at + Roda VE at de + & 1 2 + L. नर v = R. de 1.2 2 A 2 Lide + Rode az 2 ME V 2 وہے م + år + V=2. d 자 नम

Ratasional Mechanical system 02 B T So Torque Balanced IS Equation son T = Tot Tot Tk T= T; + Tot Tk Tja o dg at To م . at TK = ко T= 5 d 5 do + B.do + KO TE at So Compare Equasion 0 and
Rotational Mechanical System Electrical System

Torque(T) Voltage(V)

Moment of Inertia(J) Inductance(L)

Rotational friction coefficient(B) Resistance(R)

Torsional spring constant(K) Reciprocal of Capacitance (1/c)

Angular Displacement(θ) Charge(q)

Angular Velocity(ω)   Current(i)

from question 4 Matlab simulation

A=[1 -1 2; 0 1 0;3 2 1]

e= eig(A)

[v,d]=eig(A)

Result

A =

   1  -1   2
   0   1   0
   3   2   1

e =

   3.4495
  -1.4495
   1.0000

v =

   0.6325  -0.6325  -0.5121
        0        0   0.7682
   0.7746   0.7746   0.3841

d =

Diagonal Matrix

   3.4495        0        0
        0  -1.4495        0
        0        0   1.0000

so eigen value of the matrix is 3.4495, -1.4495, 1

corresponding eigen vector V1 =[ 0.6325

0

0.7746 ]

V2 =[ -0.6325

0

0.7746 ]

V3 =[ -0.5121

  0.7682

0.3841 ]