a) Make a function osc_energy(u, v, omega) for returning the potential and kinetic energy of an oscillating system described by (8.43)–(8.44). The potential energy is taken as 1 2ω2u2 while the kinetic energy is 1 2 v2. (Note that these expressions are not exactly the physical potential and kinetic energy, since these would be 1 2mv2 and 1 2 ku2 for a model mx
+ kx = 0.) Place the osc_energy in a separate file osc_energy.py such that the function can be called from other functions.
b) Add a call to osc_energy in the programs osc_FE.py and osc_EC.py and plot the sum of the kinetic and potential energy. How does the total energy develop for the Forward Euler and the Euler-Cromer schemes?