How to solve and plot second order differential equation using ode45?

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Studentguy
Studentguy 2023-11-23
评论： Fabio Freschi 2023-11-23
Hey there
Im trying to solve and plot the following differential equation using ode45
x''=(-2k*x-2c*x'-r*omega*(cos(omega*t)+(r/L)*cos(2*omega*t))*m+x0*M)/M+m
where
M = 22
m = 0.9
k = 25000
c = 2
omega = 860
L = 0.2
r = 0.07
The starting conditions are :
x0=0
x'0=0
I've tried a bunch of different tutorials, but keep getting different error messages.
Any help is greatly appreciated, thank you!
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Dyuman Joshi
Dyuman Joshi 2023-11-23
Is the value of x0 that appears in the ODE the same as the value of x0 that is one of the initial conditions?
Also, you have defined the variable x_speed in the ODE function, but have not used it. Is there any particular use of that variable?
Studentguy
Studentguy 2023-11-23
Ye, x0 is the same, its just part the equation i arrived at during calculations.
No x_speed isnt used anywhere.

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回答（1 个）

Fabio Freschi
Fabio Freschi 2023-11-23
编辑：Fabio Freschi 2023-11-23
Ran in:
In your code there is a mistake in the definition of x(1) and x(2)
I have made a few stylistic changes (parameters outside the function, use of implicit function) and the correction of the equations. In addition, I suggest to let ode45 to choose the timestep and keep the t vector provided as output for the plot
% clear variables, close all
x0 = [0 0];
tspan = [0 10];
% params
M = 22;
m = 0.9;
k = 25000;
c = 2;
omega = 860;
l = 0.2;
r = 0.07;
x0_speed = 0;
x0_pos = 0;
% implicit function
% changes here
% | |
% V V
dxdt = @(t,x)[x(2); (-2*k*x(1)-2*c*x(2)-r*omega^2*(cos(omega*t)+(r/l)*cos(2*omega*t))*m+x0_pos*(M-m))/M];
[t,x] = ode45(dxdt,tspan,x0);
figure
plot(t,x)
figure
plot(t,x)
xlim([0 0.5])
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Sam Chak
Sam Chak 2023-11-23
Hi @Studentguy
I double-check. The original 2nd-order differential equation in your question
is slightly different from the state equation you defined in your code:
( - 2*k*x(1) - 2*c*x(2) - r*omega^2*( cos(omega*t) + (r/l)*cos(2*omega*t) )*m + x0_pos*(M - m) )/M;
Please clarify!
Fabio Freschi
Fabio Freschi 2023-11-23
This is why I wrote my code according to the orignal equation (as stated in the comment)

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