Use only random and mathplot lib packages.DO not use numpy.

calculate$\_$LJ function that includes parameters for setting sigma

and epsom.After writing the function, perform a set of calculations with sigma

and both equal to one. Using these values, calculate the Lennard Jones potential energy for a range of distances, r$,$ from r $=0\mathrm{.}1$ to r $=5$ in increments of $0\mathrm{.}1.$ Save your results in a list.

Next, perform a set of calculations where sigma

is equal to $2$ and epsom is equal to one. Then set sigma to equal to $1$ and

epsom equal to two. For each set of calculations, save your result in a list.

Visualize all three results on a graph using matplotlib.

At least five sentences explain the steps and their importance.

Write a Python time code as example below and caluclate how much it takes to calculate module above to compare performance for n$\_$samples$=100$ and n$\_$samples$=10000000.$

Change the code to calculate the total energy for every step. Compare timings for $1,000$ steps.

import time

start $=$ time.time$()$

# put code you want to time here.

end $=$ time.time$()$

elapsed$\_$time $=$ end $-$ start

print$($elapsed$\_$time$)$