Determine the response of the system to the given initial conditions.

A 2 degree of freedom (2 DOF) system with 3 springs only is given. I am little bit confused to write the codes. I would be glad for some help.

[ 1 0 𝒙̈(𝑡) + [ 12 −2 x(𝑡) = 0 and 𝒙̇(0) = 0 , 𝒙(0) = [1 1]^𝑇

0 4] 2 12]

So here, m1=1 and m2=4 while k1=k3=10 and k2=2. But I do not know why my code is wrong.

K1=10 ; K2=2 ; K3=10 ;
M1=1   ; M2=4 ;

M= [ M1 0 ;
     0  M2] ;
K=[K1+K2  -K2;
    -K2   K2+K3] ;
[modeShape fr]=eig (K,M); %estimation of natural frequenciesand mode shapes
A00=zeros(2); A11=eye(2);
CC=[A00 A11;-inv(M)*K A00];

global CC
max_freq=max(sqrt(diag(fr))/(2*pi)); %highest frequency in Hz
dt=1/(max_freq*20);
time=0:dt:200*dt;

y0=[1 1 0 0]; %[displ1 disp2 vel1 vel2] initial condition
[tsol,ysol]=ode23('testode_2D',time,y0);
plot(time,ysol(:,1:2),'linewidth',2)

xlabel ('Time')
ylabel('displacement')
ylim([-.02 .02])
grid on

[Torsten]

According to your mathematical problem formulation, your K-matrix is wrong.

And where is testode_2D ?