%
%   compute M, K, and other model parameters of
%   double beam resonators 
%  as noted in Lecture23
%
% select the offset and use the a^2 value from Table 23.1 for  other offset 

a2 = 0.03394717776728;   % a^{2} = the coupling factor with e =  0.25 L

rho = 2330;
E = 170.e+9;
L = 40.e-6;
b = 8.e-6;
Ls= 11.8e-6;
bs = 2.7e-6;
h = 2.e-6;

A = b*h;
As = bs*h;

I = b*h^3/12;
Is = bs*h^3/12;

mb = 0.3836*rho*A*L 
ms = 0.24638*rho*As*Ls 

M = mb + a2*ms
K = 192*E*I/L^3

ks = 12*E*Is/Ls^3
K12 = a2*ks

omega  = sqrt(K/mb)/2/pi

omegas = sqrt(ks/ms)/2/pi

% compute undamped coupled resonator model;

Kc =[(K + K12)  -K12; -K12  (K + K12)];
Mc =[ M   0; 0 M];

[V, D] = eig(Kc, Mc);

freq = sqrt(diag(D))/2/pi