MATLAB by rudra pratap

146
Applications
% Fit a 1st order polynomial through (tbar , pbar)
a = polyfit (tbar ,pbar,l) ; % the output is a = [a1 aO]
% Evaluate constants pO and tau
pO = exp(a(2) );
% since a(2) = aO = log(pO)
tau = -1/a(i) ; % since al = - 1/tau
% (a) Plot the new curve and the data on l inear s cale
tnew = linspace (0,20,20) ; % create more refined t
pnew = pO*exp(-tnew/tau) ; % evaluate p at new t
plot (t,p, 'o' ,tnew ,pnew) , grid
xlabel('Time (sec) '), ylabel ('Pressure (torr) ')
% (b) Plot the new curve and the data on semilog scale
lpnew = exp (polyval (a,tnew) );
semilogy(t,p, 'o' ,tnew, lpnew) ,grid
xlabel ('Time (sec) '), ylabel('Pressure (torr) ')
% Note: you only need one plot , you can select (a) or (b) .
(a) (b)
Figure 5.6: Exponential curve fit: (a) linear scale plot, (b) semilog scale plot.
There is yet another way to fit a complicated function through your data in the
least squares sense. For example, let us say that you have time (t) and displacement
(y) data from a spring-mass system experiment and you think that the data should
follow
y = a0 cos(t) + a1tsin(t)
Here the unknowns are only ao and a1 . The equation is nonlinear in t but linear- in
the parameters a0 and a1 . Therefore, you can set up a matrix equation using each