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1. One of the most important examples of periodic motion is simple harmonic motion (SHM), in which some physical quantity varies sinusoidally. Suppose a function of time has the form of a sine wave function, y(t) = Asin(2πt / T ) (23.1.1) where A > 0 is the amplitude (maximum value).
Lecture Video: Periodic Oscillations, Harmonic Oscillators. In this lecture, Prof. Lee discusses the mathematical description of the periodic oscillation and simple harmonic oscillators. The first 5 minutes are devoted to course information.
We start this first lesson of 8.03x with the foundation of Vibrations and Waves: Simple Harmonic Motion. In this lesson we will: [mathjaxinline]\bullet [/mathjaxinline] review how to identify the forces acting on an object. [mathjaxinline]\bullet [/mathjaxinline] draw the free body diagram.
In these notes, we introduce simple harmonic oscillator motions, its defining equation of motion, and the corresponding general solutions. We discuss how the equation of motion of the pendulum approximates the simple harmonic oscillator equation of motion in the small angle approximation.
The characteristics of simple harmonic motion include: A force (and therefore an acceleration) that is opposite in direction, and proportional to, the displacement of the system from equilibrium. Such a force, that acts to restore the system to equilibrium, is known as a restoring force. No loss of mechanical energy.
We’ll start with γ = 0 and F = 0, in which case it’s a simple harmonic oscillator (Section 2). Then we’ll add γ, to get a damped harmonic oscillator (Section 4). Then add F(t) (Lecture 2). The damped, driven oscillator is governed by a linear differential equation (Section 5).
Complex Numbers and Simple Harmonic Oscillation. Lectures on Oscillations and Waves. Michael Fowler, UVa, 6/6/07. FROM A CIRCLING COMPLEX NUMBER TO THE SIMPLE HARMONIC OSCILLATOR.....................3. Describing Real Circling Motion in a Complex Way...........................................................................................3.