Help to draw a graph of a function.

There was two mistakes. I wrote in a true way. And I want anyone to help me. I studied to draw the graph of function given at the bottom of page. But my drawing is not the same as the expected figure. Please, help how can i correct my MATLAB codes.

clc; clear; clear all;
a=1;  
d0=2; 
v0=2;
nu=sqrt(2.5);
sumxx=[];
k=100;
for endp=1:k
    T=linspace(endp-1,endp,101);
    sumx=d0.*cos(nu.*T)+(v0./nu).*sin(nu.*T)+((a.*d0)./nu.^2).*(1-cos(nu.*T));
for n=0:endp-1
    K=omega(a,n,nu,v0,d0).*(1-cos(nu.*(T-(n+1))));
    sumx=sumx+(a./nu.^2).*K;
end
% sumx=sumx.*x0;
sumxx=[sumxx,sumx];
clear sumx
end
tt=linspace(0,k,k*101);
plot(tt,sumxx)
grid on
hold on

omega.m function is given below;

function w=omega(a,n,nu,v0,d0)
M=[(1-a./(nu.^2)).*cos(nu)+a./(nu.^2) sin(nu)./nu;-nu.*(1-a./(nu.^2)).*sin(nu) cos(nu)];
w=([(1-a./(nu.^2)).*cos(nu)+a./(nu.^2) sin(nu)./nu]*M-[1 0])*(M.^n)*[d0;v0];
end

My function is given like that;

and the expected figure is given like that

[Walter Roberson]

... Didn't you already ask this? I was sure I formatted this same code yesterday.

[zekeriya özkan]

Yes, I solved an equation in two ways. One of them that you formatted one of the ways yesterday, but this one which i wrote MATLAB codes above gives a different graph from that you formatted. Because of that ı asked this one.

[Walter Roberson]

One of the problems is that your k goes to 100 but the sample figure only goes to 25.

However, that does not explain why your code generates values up to roughly 4, but the sample figure only goes to about 1/2

[Walter Roberson]

The requirements are to plot over 0 <= t < m, but the piecewise definition only gives an expression for m <= t < m+1 so we do not know anything about the function over the interval that it is to be plotted over.

[zekeriya özkan]

How can i solve this problem?

Answer 1

[Sulaymon Eshkabilov]

Hi,

(1) There are some inconsistencies with the initial conditions. As given the formulations can never produce some ripples such uneven points (some uncertainties/noises are present). Since the given formulations are composed of sines and cosines, and thus, the resulting response of the system has to be a smooth plot.

(2) The shown plot is decaying process (reponse) that shows that there is significant damping > 1. With the given data, it is not a decaying process.

In implementation, some parts of the code is not correctly embeded. Here is a corrected code:

...
k=1000;
%for endp=1:k
    T=linspace(0,25, 1001);
    sumx=d0.*cos(nu.*T)+(v0./nu).*sin(nu.*T)+((a.*d0)./nu.^2).*(1-cos(nu.*T));
    for n=0:1000
        K=omega(a,n,nu,v0,d0).*(1-cos(nu.*(T-(n))));
        sumx=sumx+(a./nu.^2).*K;
    end
    % sumx=sumx.*x0;
    sumxx=[sumxx,sumx];
    clear sumx
    %end
    ...

Good luck.

[zekeriya özkan]

Thanks for answer.

Where will i enter this code to my codes?

I couldn't manage to debug these codes. Please help!

If you managed to debug these codes, can you share figure and codes?

Also let me explain that thissü solution is a solution of differential equation with piecewise constant argument. So the system is consistent inside it..

[zekeriya özkan]

Dear Sulaymon Eshkabilov;

you wrote true codes instead of my incorrect codes. I put into MATLAB those codes, but it didn't work. I wrote that codes below. The error is at figure at the bottom. Please, help to correct my errors.

a = 1;
nu = 2;
d0 = 0;
v0 = 1;
k=1000;
for endp=1:k
    T=linspace(0,25, 1001);
    sumx=d0.*cos(nu.*T)+(v0./nu).*sin(nu.*T)+((a.*d0)./nu.^2).*(1-cos(nu.*T));
    for n=0:1000
        K=omega(a,n,nu,v0,d0).*(1-cos(nu.*(T-(n))));
        sumx=sumx+(a./nu.^2).*K;
    end
    % sumx=sumx.*x0;
    sumxx=[sumxx,sumx];
    clear sumx
    end
    tt=linspace(0,k,k*101);
plot(tt,sumxx)

[Walter Roberson]

Unfortunately we cannot scroll back the image of the command window to see what MATLAB thinks the error is .

Answer 2

[Sulaymon Eshkabilov]

Hi,

Here is the complete code:

clc; clearvars;
a=1;  
d0=2; 
v0=2;
nu=sqrt(2.5);
sumxx=[];
k=1000;
    T=linspace(0,25, 1001);
    sumx=d0.*cos(nu.*T)+(v0./nu).*sin(nu.*T)+((a.*d0)./nu.^2).*(1-cos(nu.*T));
    for n=0:1000
        K=omega(a,n,nu,v0,d0).*(1-cos(nu.*(T-(n))));
        sumx=sumx+(a./nu.^2).*K;
    end
    SX=sumx;
plot(T,SX)
grid on
hold on
function w=omega(a,n,nu,v0,d0)
M=[(1-a./(nu.^2)).*cos(nu)+a./(nu.^2) sin(nu)./nu;-nu.*(1-a./(nu.^2)).*sin(nu) cos(nu)];
w=([(1-a./(nu.^2)).*cos(nu)+a./(nu.^2) sin(nu)./nu]*M-[1 0])*(M.^n)*[d0;v0];
end

[zekeriya özkan]

Dear Friend Suleyman, i am very thankfull to you. Thanks a lot. I am from TURKEY? Where are you from?

[Sulaymon Eshkabilov]

You are MOST Welcome - Ag'a! from Uzbekistan.