clear all %this clears any variables that may be in matlab's cache (unless you have a good reason, most code should begin with this)

load('data1') %This calls the your date file.

%under the assumption that the data is labeled in data1 as
%trace_x (first column of data), trace_y (second column of data)

time=trace_x; %the first column in your data file is time
d_data=trace_y(1,:);%the second column in your data is displacement

timelength=length(time);

%if you wanted the maximum displacement...
val=max(d_data');

%this finds the index (array position) of the maximum value of your data
index=find(d_data==val)
index=index(1);

%this zeros the time data and restarts time at the time of maximum displacement
time=time(index:timelength)-time(index); 

%this restarts your displacement data at the time of maximum displacement
d_data=d_data(index:timelength);

%these two parameters are our initial guesses for C, K
C0=3;
K0=2;

%we collect them in an initial parameter vector q0
q0=[C0;K0];

%this runs a matlab algorithm which searches the function cost_beam for a minimum given 
%certain input parameters...initial parameter guesses,(use help fminsearch to figure out why [] is there), time array, displacement array
%it outputs the parameters which minimize the cost and the cost
[q,cost]=fminsearch('cost_beam',q0,[],time,d_data);

%These are the optimal values for C and K
C=q(1);
K=q(2);

%Now we want to see how well the algorithm did by simulating the ode

%This is the initial [position, velocity] vector
x0=[d_data(1) 0];

%This runs one of matlab's preprogrammed ode solvers (type help ode23 in the command window and check out other solvers)
%The ode ode_model is called, the time range is given, initial [position, velocity], , and parameters
%time and [position,velocity] vectors are the outputs
[t,x]=ode23('ode_model',time,x0,[],C,K); 
%[t,x]=ode23(@(time,x0,C,K)ode_model(time,x0,C,K),x0);

%this take all rows, 1st column of x (the position) and saves it as d_model
d_model=x(:,1);

%Here we plot the collected data and compare it with the results of the model.
plot(time,d_data,'--',time, d_model,'r')
legend('experimental data','model displacement')
title('Two-parameter model estimation');
xlabel('time (s)');
ylabel('displacement');