Write a python that uses the FTCS method to solve the wave equation expressed as a set of simultaneous first-order equations for the case v = 100 m s^1, with the initial condition that (x) = 0 everywhere but the velocity (x) is non-zero, with the profile

which is a Gaussian-like profile. Here L = 1 m, d = 10 cm, C = 1 m s^1, and = 0.3 m. You will also need to choose a value for the timestep h a reasonable choice is h = 10^6 s.

A)Make a plot of the vertical displacement and its time derivative as a function of distance at time t = 0.02 s.

B)Make three plots at three different times of the vertical displacement at this transition time. Denote the time of each solution in a legend.

Screenshot results.

(x)=CL2x(Lx)exp[22(xd)2]