Energy calculations provide a powerful check on the accuracy of a numerical integration. Modify your numerical integration of the motion of a mass on a spring that you did earlier. In addition to...

Energy calculations provide a powerful check on the accuracy of a numerical integration. Modify your numerical integration

of the motion of a mass on a spring that you did earlier. In addition to plotting graphs of position versus time, also plot

graphs of kinetic energy, of spring energy, and of the sum of the kinetic energy and the spring energy, versus time during the

motion. It is up to you to choose some value for the potential energy U0 at the bottom of the well. Label the energy graphs

with numerical values and units. Make sure that the energy values are reasonable for your system.

(a) Does the sum of kinetic and potential energy remain constant as a function of time? What if you vary the step size

(which varies the accuracy of the numerical integration)?

(b) Increase the energy by increasing the initial speed. How does the amplitude A change? How does the angular

frequency ω change?