Why is there a diiference in state-space velocity and derivative of state space displacement?

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Joe on 11 Jan 2023
Commented: Mathieu NOE on 31 Jan 2023
I stumbled on this matlab code online from mathworks. However, I am surprised that the velocity (yvector(:,1)) is different from the velocity obtained from diff(yvector(:,2))./diff(t). Why des this occur? https://www.mathworks.com/matlabcentral/answers/1613980-how-can-i-obtain-the-derivative-of-a-vector-displacement-velocity-but-what-about-acceleration-i-am
clc; %command window
clear;%clear workspace
close all; % close figures
global m k
m = 80; %Defining mass of SDOF system
k = 10000;%Defining stiffness of SDOF system
dt = .02; %Defining Time Step:
t = 0:dt:4;% Defining time vector.
y0 = [0.085; 0.1]; %initial vel and disp [vel disp] %velocity.
[tsol, yvectorl] = ode45(@testode1,t,y0);
%%plot
figure()
plot(tsol,yvectorl(:,2)), title("Displacement") %Disp.(2)
figure()
plot(tsol,yvectorl(:,1)), title("Velocity") %Vel. (1)
% THIS NEEDS TO GO AT THE END OF THE FILE
%%function statespace
function dy = testode1(t,y)
global m k
dy=[-k*y(2)/m;y(1)];
end

Mathieu NOE on 11 Jan 2023
hello
where do you see a difference ?
diff or gradient based dispkacement derivatives do pretty well overlay with computed velocity
clc; %command window
clear;%clear workspace
close all; % close figures
global m k
m = 80; %Defining mass of SDOF system
k = 10000;%Defining stiffness of SDOF system
dt = .02; %Defining Time Step:
t = (0:dt:4)';% Defining time vector.
y0 = [0.085; 0.1]; %initial vel and disp [vel disp] %velocity.
[tsol, yvectorl] = ode45(@testode1,t,y0);
%%plot
figure()
plot(tsol,yvectorl(:,2)), title("Displacement") %Disp.(2)
% derivative of disp
% ddisp = [0;diff(yvectorl(:,2))./diff(t)];
figure()
plot(tsol,yvectorl(:,1),tsol,ddisp,'*r'), title("Velocity") %Vel. (1)
% THIS NEEDS TO GO AT THE END OF THE FILE
%%function statespace
function dy = testode1(t,y)
global m k
dy=[-k*y(2)/m;y(1)];
end
Mathieu NOE on 31 Jan 2023
hello
Problem solved ?

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