create sandbox and added some experiment files

experimental_setup/sandbox/s_test.m

+data = load("friction_experiment_W.dat");
+W = data(:,2);
+t = data(:,1);
+
+# At t == 68 the motor is already off
+tf = t>68;
+
+# Extract values of Omega and t when the motor is off
+W_off = W(tf);
+t_off = t(tf);
+
+# Omega has NaN values, remove them!
+idx   = find (!isnan(W_off));
+t_off = t_off(idx);
+W_off = W_off(idx);
+
+n = length (W_off); % length of data
+
+# calcjulate time derivative from a smoothed signal
+# This part changes when using the signal package.
+# Check butter, fitlfilt and sgolayfilt.
+
+%Ws           = postpad (spencer (W_off), n);
+%idx          = find (Ws!=0);
+%Ws           = Ws(idx);
+%ts           = t_off(idx);
+
+pkg load signal
+ln            = 21;
+Ws            = sgolayfilt (W_off, 1, ln);
+idx           = (2*ln):(n-2*ln+1);
+Ws            = Ws(idx);
+ts            = t_off(idx);
+
+# Take derivative using diff
+dWsdt        = diff (Ws) ./ diff (ts);
+dWsdt(end+1) = dWsdt(end);
+
+figure(1)
+subplot(2,1,1)
+plot(t_off,W_off,'or;Omega;',ts,Ws,'-b;Smoothed;');
+axis tight
+ylabel('signal')
+
+subplot(2,1,2)
+plot(ts,dWsdt,'or;dW/dt smooth;');
+axis tight
+xlabel('time')
+ylabel('signal')
+
+[alpha, S] = polyfit(Ws, dWsdt, 2);
+alpha_err  = sqrt (diag (S.C) / S.df) * S.normr;
+
+figure(2);
+plot (Ws, dWsdt, 'og', Ws, polyval(alpha,Ws),'-k');
+axis tight
+xlabel('Omega')
+ylabel('Omega dot')
+
+