Problem $1(15$ points$)$:$$Consider the simple pendulum discussed in the class:$+$sin $=0,0<<$And the initial conditions are $(0)=,=0.$Write a computer program to numerically solve this nonlinear equation using Euler's $($forward$$difference$)$ finite difference scheme. I suggest using MATLAB or Python. Take $=2\mathrm{.}0,=32\mathrm{.}2,=4$ in the numerical computation.$$Plot and tabulate the numerical results for two different time steps $\backslash$Delta $=0\mathrm{.}05,\backslash$Delta $=0\mathrm{.}025$along with the exact linear solution.$$For submission, you need to provide a figure like the one we showed in class that compares the$$numerical solutions $()$ with the analytical solution of the simple pendulum $($linearized$$equations$).$ You also need to submit the MATLAB $($Python$,$ or any other coding language$)$codes you used to calculate the results.