ans =
Hi @DP
A 5-coupled mass-spring-damper network constitutes a 10th-order system. If you are referring to the 'frequency equation' as the Laplace transfer function, we can utilize the 'charpoly' and 'tf' functions. Additionally, the 'damp()' command can provide you with information about the system's natural frequencies.
Update: Check if you want to find the natural frequencies of the mass-damper-spring system using this approach:
m1 = 1;
m2 = m1;
m3 = m1;
m4 = m1;
m5 = m1;
c2 = 2*m1/100;
c3 = c2;
c4 = c2;
c5 = c2;
k2 = m1/1.1486;
k3 = k2;
k4 = k2;
k5 = k2;
% Construct mass matrix
M = [m1, 0, 0, 0, 0;
0, m2, 0, 0, 0;
0, 0, m3, 0, 0;
0, 0, 0, m4, 0;
0, 0, 0, 0, m5];
% Construct damping matrix
C = [c2, -c2, 0, 0, 0;
-c2, c2+c3, -c3, 0, 0;
0, -c3, c3+c4, -c4, 0;
0, 0, -c4, c4+c5, -c5;
0, 0, 0, -c5, c5];
C = 1000*C;
% Construct stiffness matrix
K = [k2, -k2, 0, 0, 0;
-k2, k2+k3, -k3, 0, 0;
0, -k3, k3+k4, k4, 0;
0, 0, -k4, k4+k5, -k5;
0, 0, 0, -k5, k5];
%% state matrix
% A = [zeros(size(M)), eye(size(M));
% -M\K, -M\C]
% CE = charpoly(A);
% Gp = tf(1, CE)
% damp(Gp)
%% Eigenvalues
lambda = eig(M\K)
%% Natural frequencies of the system
omega = sqrt(lambda)
