MATLAB: Second time derivative of function

derivativedifferentiationsecondsecond derivative

I have defined a model of displacement 'x' and represented its first derivative with 'v' using the code below. However, when I want to differentiate 'v' using the same function it does not work. Is there a different approach to differentiating derivatives in MATLAB? here is the code:
h = 60 ; 
b =130 ; 
r = 28 ; 
w = 2*pi; % angular velocity
t =0:(1/36):1 ; 
x = b*(r*sin(w*t))./(h-r*cos(w*t));
v = diff(x)./diff(t) ;   % derivative of x w.r.t t
a = diff(v)./diff(t) ;   % derivative of v w.r.t t

Best Answer

It does not work, because the length of diff(x) and diff(t) are not the same. diff function takes the difference between each element. However returns 1 element less than the original vector since there is no way to find the difference for the last element.
Since you have fixed step size you can use
v = diff(x)./(1/36); 
td = t(1:end-1); % time vector for plotting first derivative
a = diff(v)./(1/36) ;tdd = t(1:end-2)    
tdd = t(1:end-2); % time vector for plotting second derivative
Alternatively you might try symbolic toolbox to derive the derivative of the expression symbolicly and then plug in numbers.
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