FFT, acceleration-frequency, vibration

Hello everybody ;

I have torsional angle values and axial displacements.

I first try to draw the acceleration-frequency graph by taking the derivative of values first and then applying fft.

I'm trying to figure out where I made a mistake at Matlab.

When I thought that the graph I had drawn was correct, my friend calculated it using Phayton,

and our results turned out very different, and his are quite close to the correct one.

I'm trying to figure out where I made a mistake at Matlab.

I would be glad if you help.

%% For two times derivatives
t=t1(1:end-2);
t_step = 0.005;
v=diff(x1)./t_step;
a=diff(v)./t_step;

%% for fft

ts=1/t_step;
N2=2^nextpow2(length(a));
freq2=(0:1:(N2-1)/2)*ts/N2;
fx1=fft(a,N2)/N2*2;
ffx1=abs(fx1(1:floor(N2/2)));
plot(freq2,ffx1),xlabel('Frequency (Hz)'), ylabel('Acceleration (m/s^2)')