function [cost,d_model]=cost_beam(q0,time,d_data)
%The function defines a cost function for the vibrating beam inverse problem
%It requires as inputs a vector of parameters, time, and your collected data.
%Recall that the inputs are dummy variables.  That is to say that even though 
%'time' appears here, it may not be the same 'time' as from inv_beam, it is 
%only what is sent through the function.

C=q0(1);
K=q0(2);
x0=[d_data(1) 0]; %initial conditions [position, velocity]


%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); 
d_model=x(:,1); %This gives the positions of the beam.

%Here the cost is actually calculated.
cost=sum((d_data(:)-d_model(:)).^2);