Build a computational model of a simple hanging harmonic oscillator using the Euler method. Use realistic values for the parameters (i. e., � and � such that the period is reasonable). Assume the mass of the spring is negligible compared to the attached mass, and that the harmonic oscillator has been stretched vertically downward a distance �!, relative to its hanging equilibrium position and released from rest. Produce graphs of the position and velocity of the mass as a function of time, and compare these with the exact functions for the position and velocity, �(�) = �!cos)*� � �- and �(�) = −*� � �!sin)*� � �-, that result from solving Newton's 2nd law analytically. Does the angular frequency match that expected for a simple harmonic oscillator of mass � and spring constant �?