This question must be solved using MATLAB For given 2nd orde

This question must be solved using MATLAB.

For given 2nd order ODE x(t) + 2 omega_n xi x (t) + omega_n^2 x(t) = f(t): Find the convolution kernel Utilizing MATLAB built-in function trapz implement a MATLAB function that takes f(t), m, c and k and a valid time interval and returns x(t))name your function DuhamelFcn) Using your DuhamelFcn solve the following ODE for xi = 0.05 and omega_n = 2: x(t) + 2 omega_n xi x(t) + omega_n^2 x(t) = sin(t), x(0) = 2, x(0) = 0 Solve the above equation analytically Using MATLAB plot results of part 3 and 4. For this problem you need to submit your MATLAB code in CCLE.

Solution

In MATLAB convolution function in used to do the 2-D CONVOLUTION .it has three parameter the input array the kernel and a string defining the size of the output .there are 3different modes:

1)option same outputs an array of the same size as the input

2)option full gives back the whole result

3)option valid returns those elementsonly which were fully covered so there was no sliding off during the windowing