Question

Simple Hanging Harmonic Oscillator Developed by K Roos In this set of exercises the student builds a computational model of a hanging mass-spring system that is constrained to move in 1D, using the simple Euler and the Euler-Cromer numerical schemes. The student is guided to discover, by using the model to produce graphs of the position, velocity and energy of the mass as a function of time, that the Euler algorithm does not conserve energy, and that for this simple oscillatory system, a modified algorithm (Euler-Cromer) is necessary to avoid artificial behavior in the model. Exercises Exercise 1: Euler Algorithm Model of a S HO Build a computational model of a simple hanging harmonic oscillator using the Euler method. Use realistic values for the parameters (i.e., spring constant k and attached mass m, such as would be encountered in a typical introductory mechanics laboratory exercise. Also, assume that the mass of the spring is negligible compared to the attached mass, and that the harmonic oscillator has been stretched vertically downward a distance yo, relative to its hanging equilibrium position and released from rest. Use the model to 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 and that result from solving Newton's 2nd Law analytically. Does the angular frequency match that expected for a simple harmonic oscillator of mass m an spring constant k?

Answer 1

Given -Yo

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