Question

Please use python!
Work out a formula for the total energy (kinetic plus gravitational) of the pendulum in term of 8 and w and constants. Take the gravitational potential energy to be zero at the lowest point of the pendulum swing. Write your equation below using Markdown and Latex

Write a function to calculate the energy using the trajectories produced by any of the previous functions. Plot the total energy for at least 10 perios for trajectories produced by Euler, Euler-Cromer, Leapfrog and Runge Kutta

Answer 1

kinetic energy = 1/2 m (²+ ²)

= 1/2 m ( L² COS² + L² Sin²) ² (X=LSin θ and y=LCOSθ)

  = 1/2 m L²²

  = 1/2 m L^{2 2} ( = )

change in potential energy = mgh

= mg (L- L COS θ)

= mgL (1- COS θ )