Hi folks, I have to use difference equation to find second derivative of sin function. This is the function g1*sin(2*pi*t/T). I use approximation with central finite difference of second order with second-order accuracy. It's it fpp(x) = ( f(x+h) -2f(x) + f(x-h) ) / h^2.... When i wrote simple program to prove that this approximation works, and it is:
clear, clc % params of sin function t = 0:0.01:1; Ts = 0.01; g1 = 0.6; T = 0.2; % the second order differential of sin function tpp = -4 * g1 * pi^2 * sin(2 * pi * t / T) / T^2; % the second order difference of sin function tdd = (sin(2 * pi * (t+Ts) / T) - 2*sin(2 * pi * t / T) + sin(2 * pi * (t-Ts) / T)) /Ts^2; % plot the result plot(t, t1dpp, '-b', t, t1dd, '-r')
Then I plotted the result the sins are different - with differential equation the Amp it (-600; 600) and with difference it's (-1000; 1000). I'm new to difference equation i try to do my best, but i can't managed with this problem. Can someone help me ? I need the approximation to be same as the second derivative of sin function. Thanks !