Question

Compute second derivative O solutions submitted (max: 10) You are provided with a set of data for the position of an object over time. The data is sampled at evenly spaced time intervals. Your task is to find a second order accurate approximation for the acceleration at each point in time. Write a Matlab function that takes in a vector of positions x, the time interval between each sampled point h, and outputs the acceleration vector a. You will need to look up the one-sided difference formulas for the second derivative. One reference is provided here. Note that this function can be interpreted more generally: input x, output x, no matter the interpretation of x or t. Function C Reset MATLAB Documentation i function a = secondDeriv(x,h) 2 % Use och^2) approximations to compute second derivative 3 % x = evenly spaced data 4 % h = spacing between data points i.e. Delta t 5 % a = second derivative of x with respect to t Code to call your function Reset 1 h = 0.1; 2 t = 0:h:2*pi; 3 x = sin(t) + t.^2; 4 a = secondDeriv(x,h); plot(t,a) % should look like -sin(t)+2
My code for calculating the first derivative is the second image

Answer 1

1 2 3 4 5 6 7

>> h=0.1; >> t = 0:h:2*pi; >> X =sin(t) +t. 2; >> a = second_Deriv(x,h); >> hold on; >> plot(t, a) >> plot(t, 2-sin(t))

i 3 4 function v = first_Deriv(x, h) t = length(x); v = zeros (1,t); v (1) = (-3*x(1) + 4*x (2) - x(3))/(2*h); v(t) = (3*x(t) - 4*x(t-1) + x(t-2))/(2*h); 7 for i=2: (t-1) 8 v(i) = (x(i+1)-x(i-1))/(2*h); 9 Fend 10 Lend

i 2 3 function a = second_Deriv(x, h) v = first_Deriv(x,h); a = first_Deriv(v, 1); end 4

Code

function a = second_Deriv(x,h)

v = first_Deriv(x,h);

a = first_Deriv(v,h);
end