Need Help Transcribing differential equations in to Matlab code

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JB 2018-7-6

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关闭： MATLAB Answer Bot 2021-8-20

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.

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Answer 1

Fabricio Castro 2018-7-7

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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

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Star Strider 2018-7-7

@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 2018-7-7

@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