Write a program to generate an appropriate curve fitting function for a quadratic fit. Validate your program using a dataset with a minimum of $30$ entries. Also program should be provide a table of dataset values, fitted function and error on each data point.

Write a generalized code for the diagonalization of matrix using the Gauss$-$Jordan elimination method.

$($a$)$ Generate $100,1000$ and $10000$ random numbers between $25$ to $75.($b$)$ For these given datasets, establish the central limit theorem using a computer code.

Write a program to calculate the kinetic energy, potential energy, total energy and velocity of a particle of mass $m$ falling freely under gravity.

Write a program to calculate the trajectory of a projectile of mass $m,$ initial velocity $v,$ and initial angle $.$

Write a program to describe the simple harmonic motion of an object of mass m $.$

Write a program for coupled harmonic oscillator $($last derivation in slides of module $5).$