Need to plot a graph of -y(t) and x(t) on MATLAB

I dont know what im doing if im being honest and i really need help. I need to plot a graph of -y(t) and x(t).

function [t,x,pos]=lab1(r0,k)
% assume pendulum mass m=1
m=1;
dt=0.01;        % integration time step
tspan=0:dt:500; % timespan of integration from 0 to 500
opt=odeset('Reltol',1e-9,'AbsTol',1e-9);
x0= input('enter initial condition in the form of [xinit0;vxinit0;yinit0;vyinit0] : ');
x0=[r0;0;0;0];
[t,x]=ode45(@pend,tspan,x0,opt,k,m,r0);
pos(:,1)=x(:,1).*sin(x(:,3));
pos(:,2)=-x(:,1).*cos(x(:,3));
function RHS=pend(t,x,k,m,r0)
r=sqrt(x(1)^2+x(3)^2);
dr=r-r0;
RHS(1,1)=0;
RHS(2,1)=0;
RHS(3,1)=0;
RHS(4,1)=0;
end
 
end

[Stephen23]

Original question by Paul Jones retrieved from Google Cache:

http://web.archive.org/web/20210218180946/https://webcache.googleusercontent.com/search?q=cache%3ADTDdXl4nazcJ%3Ahttps%3A%2F%2Fwww.mathworks.com%2Fmatlabcentral%2Fanswers%2F748772-need-to-plot-a-graph-of-y-t-and-x-t-on-matlab-for-a-dynamics-problem

Need to plot a graph of -y(t) and x(t) on MATLAB for a Dynamics Problem

I dont know what im doing if im being honest and i really need help. I need to plot a graph of -y(t) and x(t).

function [t,x,pos]=lab1(r0,k)
% assume pendulum mass m=1
m=1;
dt=0.01;        % integration time step
tspan=0:dt:500; % timespan of integration from 0 to 500
opt=odeset('Reltol',1e-9,'AbsTol',1e-9);
x0= input('enter initial condition in the form of [xinit0;vxinit0;yinit0;vyinit0] : ');
x0=[r0;0;0;0];
[t,x]=ode45(@pend,tspan,x0,opt,k,m,r0);
pos(:,1)=x(:,1).*sin(x(:,3));
pos(:,2)=-x(:,1).*cos(x(:,3));
function RHS=pend(t,x,k,m,r0)
r=sqrt(x(1)^2+x(3)^2);
dr=r-r0;
RHS(1,1)=0;
RHS(2,1)=0;
RHS(3,1)=0;
RHS(4,1)=0;
end
 
end

[Adam Danz]

@Paul Jones in response to your flag, perhaps providing the URL to the question/answer that helped you would be helpful to others in the future.

[Rik]

You're just being rude by removing your question. That makes me suspect you are trying to avoid cheating detection.

[Adam Danz]

@Paul Jones

In regards to Rik's comment, please see a related comment of mine within another thread that explains why the request to remove content sets off the cheating detectors and the risk of plagiarized content. Are you planning on citing Alan Stevens or Steven Lord?

[Paul Jones]

I will cite Alan Stevens.

[Paul Jones]

@Rik

Responding to Rik's comment. I am not trying to avoid cheating detection. For the assignment that I am working on I was given clear persmission by my instructor to use this website to get help as a lot of student do not know how to use MATLAB properly. The main goal of the assignment is to be able to formulate a report that discusses the relation of the dynamics problem to the results and not how the results were generated. I will cite any information that I may or may not use in my final report.

[Paul Jones]

@Adam Danz

After viewing your related comment I do not want to remove this post anymore as it could still help others. I am sorry for any confusion related to this I did not mean to be rude or anything my intentions were not ill.

[Rik]

I expect I also speak for Adam in this: No problem, feel free to restore your question to the original state.

[Paul Jones]

@Rik Excuse my lack of experience, but how do I do that? (I'm not sure how to use this website properly)

[Rik]

You can edit your question to make it look like the original again. There is currently no direct option to restore a previous version other than to edit your question and put back the same information.

[Adam Danz]

Thanks @Paul Jones

Answer 1

[Alan Stevens]

Here are the equations that you will need to include in your pend function.

Now let's see you implement them!

Answer 2

[Steven Lord]

pos(:,1)=x(:,1).*sin(x(:,3));
pos(:,2)=-x(:,1).*cos(x(:,3));

So pos(:, 1) is the x(t) you're trying to plot and pos(:, 2) is the -y(t)? If so just call the plot function.

plot(pos(:, 1), pos(:, 2))

[Alan Stevens]

Here's the syntax using the equations I generated. You should be able to modify this to use your equations if you think they are correct:

% Data
r0 = 5;   % m
k = 10;   % N/m
m = 1;    % kg
g = 9.81; % m/s^2

dt = 0.1; % s
tspan = 0:dt:20; 

% Initial conditions
xy0 = [r0, 0, 0, 0];   % [x0 y0, vx0, vy0]
[t, xy] = ode45(@(t,xy) rates(t,xy,r0,k,m,g), tspan, xy0);

x = xy(:,1); y = xy(:,2);
vx = xy(:,3); vy = xy(:,4);

plot(t,x,t,-y),grid
xlabel('t'),ylabel('x and -y')
legend('x','-y')

function dxydt = rates(~,xy,r0,k,m,g)

        x = xy(1); y = xy(2);
        vx = xy(3); vy = xy(4);
        r = sqrt(x^2+y^2);
        theta = atan(-x/y);
        dxydt = [vx;
                 vy;
                 -k/m*(r-r0)*sin(theta);
                 -g+k/m*(r-r0)*cos(theta)];
 
end

The above results in

[Alan Stevens]

I put nothing at the beginning - it's a script in its own right.