Module 15  Particle Motion and Parametric Models 
Introduction  Lesson 1  Lesson 2  Lesson 3  Self Test 
Lesson 15.2: Harmonic Motion 
Motion along a straight line was illustrated in Lesson 15.1. This lesson will explore harmonic motion, that is, motion that oscillates. Simple harmonic motion is motion that can be modeled by either of the following functions, where t represents time and a, b, c, and d are constants: The Motion of a Particle Suppose that a particle moves along the vertical line x = 1 according to the equation below, where y represents the height of the particle above the ground and t is time in seconds. Modeling the Particle's Motion The motion of the particle from t = 0 to t = 5 seconds can be modeled using parametric equations.
You should see the particle rise and fall along the vertical line x = 1.
15.2.1 What is the effect of this change on the graph? Click here for the answer. Another Model Add the following pair of equations to the Y= editor to produce another model for the particle motion.
15.2.2 Use the Trace feature on the second graph to determine when the particle is moving upward during the first five seconds. Click here for the answer. 15.2.3 When is the particle moving downward during the first five seconds? Click here for the answer. 15.2.4 When is the particle momentarily at rest (velocity is zero) during the first five seconds? Click here for the answer. Graphing the Derivative Add the following equations to the Y= editor to see the derivative (instantaneous velocity) of the particle.
15.2.5 Use Trace on the velocity curve to find the first time the particle is momentarily at rest. Click here for the answer. 15.2.6 How does the derivative indicate when the particle is moving upward or downward? Click here for the answer. 
< Back  Next > 
©Copyright
2007 All rights reserved. 
Trademarks

Privacy Policy

Link Policy
