Anyone to help (I just need to know in what order initial conditions are put and the order of columns solution vector) !!!!!!!!!!
I need to know the order of solution vector i-e how solution is stored in solution vector of coupled 2nd order differential equations
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I have these two coupled differential equations
m_1 * z_1_dot_dot + (k_1+k_2 ) z_1 + b * z_1_dot = k_2 * z_2 + b * z_dot_2
m_2 * z_2_dot_dot + k_2 z_2 + b * z_2_dot = k_2 * z_1 + b * z_1_dot + f
( 2 Degree of freedom mass spring system with damping in between Attached image )
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1071505/image.jpeg)
Now I have written a code for the solution of these two coupled diffferential equations but I dont know how to write correct initial conditions order (z1 , z_1_dot , z_2 , z_2_dot)
And also I dont know in what order the solution is stored in Solution vector i-e which columns contains the z1 displacement and velocity and which columns contain the displacement and velocity of second z2 (z_2 and z_2_dot)
Here is the Code
clc
clear
close all
% Use Symbolic toolbox
syms m1 m2 k1 k2 f b z1(t) z2(t) t Y;
dz1 = diff(z1);
d2z1 = diff(z1,2);
dz2 = diff(z2);
d2z2 = diff(z2,2);
% Write two Coupled Differential Equations
Eq1 = d2z1 == (k2*z2(t) + b*dz2 - (k1+k2)*z1(t) - b*dz1)/m1; % 1st Equation
Eq2 = d2z2 == (k2*z1(t) + b*dz1 + f - k2*z2(t) - b*dz2)/m2;
% Convert the equations to vector Field (Coupled first order linear differential equations)
[VF,Subs] = odeToVectorField(Eq1, Eq2);
ftotal = matlabFunction(VF,'Vars',{t,Y,m1,m2,k1,k2,f,b});
% Define the Known Parameters
m1 = 10;
m2 = 5;
k1 = 40;
k2 = 20;
b = 10;
f = 5;
% Use ode45 Command to solve the system of coupled equations
tspan = [0 20]; % Choose Appropriate Simulation Time
ic = [0 0 0.3 2]; % Choose Appropriate Initial Conditions (% This is where I need Help The conditions are m1 initial displacement "0.3" and velocity of "2" and for m2 both are zero How do I write in Correct Order)
[t,y] = ode45(@(t,y) ftotal(t,y,m1,m2,k1,k2,f,b), tspan, ic);
% Here t is time vector and y is the solution vector containing solution to
% differential equations
Please please Anyone help and also please make me understand to avoid this confusion in Future.
Any Type of help would be EXTREMELY APPRECIATED !!!!! ( I have given the code which works)
Accepted Answer
Sam Chak
on 20 Jul 2022
Edited: Sam Chak
on 20 Jul 2022
@Haseeb Hashim, Aha, I see.
You will have to remove the semicolon at the end of this line
[VF,Subs] = odeToVectorField(Eq1, Eq2);
so that the output Subs can be displayed and you will know the sequence of the system states. Refer to
For example,
syms f(t) g(t)
eqn1 = diff(g) == g-f;
eqn2 = diff(f,2) == g+f;
eqns = [eqn1 eqn2];
[V,S] = odeToVectorField(eqns)
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