Exercise 1: Euler Algorithm Model of a SHO Build a computational model of a simple hanging harmonic oscillator using the Euler method with MATLAB. 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 y0, 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, y(t) = y0 cos   s k m t   and v(t) = − s k m y0 sin   s k m t   , 1 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?

In a voltaic cell, electrons flow from the (positive/negative) to the (positive/negative) terminal.

5submission this assignment is worth 20 points total. you are required to submit the following by next lab: 1. (3 points) determine the equation for the output angular velocity ω2 = θ˙ 2 as a function of θ1, ω1 = θ˙ 1 and α. you must show all your work to receive credit. 2. (2 points) use the result of problem#1 to plot ω2 over 0 ≤ θ1 ≤ 360deg with ω1 = 360deg/sec. do this for α = {10,30}deg. show the results on the same plot and properly label the axes, title, legend. for this you can use matlab or ms excel. 3. (3 points) determine the equation for the output angular acceleration ω˙ 2 and create a plot similar to the one in problem#2. 4. (10 points) submit plots of the results (ω2 and ω˙ 2) obtained from creo/mechanism and compare them to results of problem#2 and problem#3. note that you should do these comparisons for the two cases with α = {10,30}deg. 5. (2 points) provide a brief explanation of the results. did they match? what are the implications as misalignment angle increases?

What is the measurement of how fast an object moves relative to a reference point?