Question

In matlab, us the pseudo inverse function to create a linear fit from velocity-second matrix. Use the equation to project the speed when v=12 m/s.

v [6 8 10]
s [50 88 124]

Answer 1

Script file:

clear all;
clc;
n=1;
% n=order of polynomial
% given data
v=[6 8 10];
s=[50 88 124];
% after linearising
% v = a(1) + a(2)*s
X=v;
Y=s;
m=length(X);
if size(X)~=size(Y)
    error('Enter X and Y in same order');
end
A=zeros(n+1,n+1);
B=zeros(n+1,1);
for i=0:n
   for j=0:n
      A(i+1,j+1)=sum(X.^(i+j));
      B(i+1)=sum((X.^(i)).*Y);
   end
end
a=A\B;
fprintf('The polynomial equation is \ns=');
fprintf('%f+%f*v\n',a(1),a(2));
fprintf('At v=12, s=%f',a(1)+a(2)*12);

Screenshot:

1 clear all; 2 clc; 3 n=1; 4% n=order of polynomial 5% given data 6 v=[6 8 10]; 7 S=[50 88 124]; 8% after linearising 9% v = a (1) + a (2)*s 10 X=V; 11 Y=S; 12 m=length(X); 13 if size (X)~=size(Y) 14 error('Enter X and Y in same order'); 15 end 16 A=zeros (n+1, n+1); 17 Brzeros (n+1,1); 18 for i=0:n 19 for j=0:n 20 A(i+1, j+1)=sum (X.^(i+j)); 21 B(i+1)=sum((X.^(i)). *Y); 22 end 23 end 24 a=A\B; 25 fprintf('The polynomial equation is \ns='); 26 fprintf('%f+%f*v\n',a(1),a(2)); 27 fprintf('At v=12, s='f',a(1)+a(2) *12);

Save the above program and execute it.

Result:

The polynomial equation is S=-60.666667+18.500000*v At v=12, s=161.333333

I hope this will help you.