MATLAB Answers

Finding the velocity from displacement

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Adam on 19 Nov 2011
Hi guys,
I'm trying to model a jump, using simulink I've found the displacement ( height vs. distance), I'm trying to find the velocity and acceleration of the jump. I've tried to use a derivative block, where I've inserted after my transfer block it (between the y displacement and my XY graph). The velocity isn't coming out right, and reducing the size of the step size doesn't seem to be helping.
Could anyone give me any advice?
I can attach the m file or a screenshot if needed.
Abhishek Gupte
Abhishek Gupte on 11 Jan 2012
Take a look at the demo model sldemo_bounce. It might help.

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Answers (3)

Dr. Seis
Dr. Seis on 12 Jan 2012
This is a function I wrote to convert seismograms from one domain to another:
function dataout = iomega(datain, dt, datain_type, dataout_type)
% IOMEGA is a MATLAB script for converting displacement, velocity, or
% acceleration time-series to either displacement, velocity, or
% acceleration times-series. The script takes an array of waveform data
% (datain), transforms into the frequency-domain in order to more easily
% convert into desired output form, and then converts back into the time
% domain resulting in output (dataout) that is converted into the desired
% form.
% Variables:
% ----------
% datain = input waveform data of type datain_type
% dataout = output waveform data of type dataout_type
% dt = time increment (units of seconds per sample)
% 1 - Displacement
% datain_type = 2 - Velocity
% 3 - Acceleration
% 1 - Displacement
% dataout_type = 2 - Velocity
% 3 - Acceleration
% Make sure that datain_type and dataout_type are either 1, 2 or 3
if (datain_type < 1 || datain_type > 3)
error('Value for datain_type must be a 1, 2 or 3');
elseif (dataout_type < 1 || dataout_type > 3)
error('Value for dataout_type must be a 1, 2 or 3');
% Determine Number of points (next power of 2), frequency increment
% and Nyquist frequency
N = 2^nextpow2(max(size(datain)));
df = 1/(N*dt);
Nyq = 1/(2*dt);
% Save frequency array
iomega_array = 1i*2*pi*(-Nyq : df : Nyq-df);
iomega_exp = dataout_type - datain_type;
% Pad datain array with zeros (if needed)
size1 = size(datain,1);
size2 = size(datain,2);
if (N-size1 ~= 0 && N-size2 ~= 0)
if size1 > size2
datain = vertcat(datain,zeros(N-size1,1));
datain = horzcat(datain,zeros(1,N-size2));
% Transform datain into frequency domain via FFT and shift output (A)
% so that zero-frequency amplitude is in the middle of the array
% (instead of the beginning)
A = fft(datain);
A = fftshift(A);
% Convert datain of type datain_type to type dataout_type
for j = 1 : N
if iomega_array(j) ~= 0
A(j) = A(j) * (iomega_array(j) ^ iomega_exp);
A(j) = complex(0.0,0.0);
% Shift new frequency-amplitude array back to MATLAB format and
% transform back into the time domain via the inverse FFT.
A = ifftshift(A);
datain = ifft(A);
% Remove zeros that were added to datain in order to pad to next
% biggerst power of 2 and return dataout.
if size1 > size2
dataout = real(datain(1:size1,size2));
dataout = real(datain(size1,1:size2));
Sohaib Sulehri
Sohaib Sulehri on 21 Feb 2018
Hi x, Can you explain the way you are calibrating and filtering you data. Moreover, which accelerometer are you using?

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Guy Rouleau
Guy Rouleau on 12 Jan 2012
I like to use a filtered derivative to do that.
A transfer function in the form s/(tau*s+1)^2 with the right "tau" will give you something close to "s" for low frequency and close to "1" for high frequency, limiting that spike that you probably see in your model.
You can find some doc on that in the SimMechanics doc:

Dr. Erol Kalkan, P.E.
Dr. Erol Kalkan, P.E. on 11 Jul 2019
This algorithm finds the corner filter frequencies based on the frequency content. It has been already implemeted to the USGS's PRISM software (

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