Need Help Transcribing differential equations in to Matlab code

I am trying to transcribe the following differential equation that describes a falling body:

dy/dt=mg/K (1-e^(-K/m t)) (with air resistance)

dy/dt=gt (without air resistance)

I would like to create a function and then call the function using ode45 and then plot a graph. I am still trying to get a good handle of matlab, but I have not been successful.

Answer 1

[Fabricio Castro]

Hi JB

Your problem is kind of simple to solve. With the following code you will achieve what you want:

%Supose you may want to use a time interval of [0,3] with an initial
%condition y0 equal to 50 meters

timeInterval = linspace(0,3,51);
y0 = 50;

%Defining parameters like mass (m), air resistance (K), and gravity (g)
m = 5;
K = 2;
g = 9.8;

%Using ode45 function to solve the falling body equation
[t,y] = ode45(@(t,y) (m*g)/(K*(1-exp(-K/(m*t)))), timeInterval, y0);

%Plot the result
figure
subplot(1,2,1)
plot(t,((m.*g)./(K.*(1-exp(-K./(m.*t))))),'-bo')
xlabel('time')
ylabel('dy/dt')
title('ODE graph')
set(gca,'FontSize',18)
subplot(1,2,2)
plot(t,y,'-ro')
xlabel('time')
ylabel('y')
title('Solution graph')
set(gca,'FontSize',18)

Thanks

[Star Strider]

@Fabricio Castro — We do not supply complete code to homework problems here on MATLAB Answers. The OP must demonstrate an effort. We will then help to get the posted code running.

[JB]

@Star_Strider - I appologize. Here is my first attempt at the code:

"func1.m" file: function dy = func1(t, y) dy = (m*g)/(K*(1-e^(-K/(m*t)))); end

Then calling it using ode45: [t,y] = ode45(@func1, [I have no Idea what I am doing here], y0);

I will remember to post my first attempt in my next question.

Sorry about that.

@Fabricio_Castro - Thank you for the assistance. As you can see, I am trying to create a function of the equation and then call it using ode45 and the plot the graph.

Any assistance would be greatly appreciated. I am very new to Matlab.

V/R JB

Answer 2

[Star Strider]

The syntax of your function is correct. However you need to spend some time with the documentation.

Specifically see the documentation on the exp (link) function.

For future reference, see the documentation on Anonymous Functions (link), and Vectorization (link).