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Lecture 14: Oscillations
October 12, 2017
Reading Assignment
- Read: Chapter 13
- Study: Ex 13.1; Figs 13.5, 13.6, 13.7; Ex 13.2; Figs 13.19, 13.20
Objectives
- (Continuing objective) Relate the concepts of relativity, momentum, and oscillations to “everyday” situations and discuss various applications of the concepts to practical problems in various fields of science, medicine and engineering.
- Given an equation x(t) for a simple harmonic oscillator, determine the frequency f, period T, angular frequency ω, amplitude A, phase constant \phi, and maximum speed and acceleration for the oscillator. Conversely, write down the equation for x(t) given enough of these quantities.
- Use conservation of energy to relate position and speed of an undamped oscillator at one moment to position and speed at a different moment.
- Use Newton's second law to determine the acceleration for a simple harmonic oscillator in the form $a_x=-(\mbox{const})x$. From this determine the angular frequency of oscillation.
- Be able to explain (in your own words) the concept of resonance for a forced oscillator, and be able to approximate the resonant frequency, either from a resonance curve or from information about free (unforced) oscillations of the same system.
Homework
- Friday's Assigned Problems: A59; CH 13: 8, 19, 23, 25, 39, 41, 43, 59, 71
- Monday's Hand-In Problems: A61; CH 13: 22, 32, 34, 72
Lecture Materials
- Click here for the Lecture overheads
or here for full-sized version.
Answers to ConcepTests: (1) a -- 3, b -- 6, c -- 3; (2) 3; (3) 2; (4) 3; (5) a -- 1 or 6; b -- 3 or 5
Videos of example problems
To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.- Video Example #1: Determining the period of oscillation for systems of springs and masses.
- Video Example #2: Conservation of energy.
Oscillations and resonance in PHYS 211 tomorrow. https://t.co/j0Ae6YT4n0 #IsItLiveOrIsItMemorex
— Tom Solomon (@TheChaoticBird) October 13, 2016
Pre-Class Entertainment
- Love is the Drug, by Roxy Music
- L.A. Woman, by the Doors
- Land of Canaan, by the Indigo Girls
- L.S.F., by Kasabien