January 2012
Intermediate to advanced
448 pages
9h 47m
English
Content preview from Mechanical and Electromagnetic Vibrations and Waves
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
Chapter 2
Superposition of Harmonic Oscillations, Fourier Analysis
The oscillations of a system can never be exactly periodic since they always have a beginning and an end. However, the oscillations may be treated as approximately periodic if they last a very long time, compared to the period of a single oscillation. On the other hand, even if the oscillations of a system are approximately periodic, they are never exactly simple harmonic (i.e. represented by a sinusoidal function with a single frequency). For instance, even if light is a single line of the discrete atomic spectrum or a laser beam, it is always a superposition of monochromatic waves in a more or less wide band. The superposition of oscillations and waves is so real and important that it is often raised to the rank of a principle (called the superposition principle). It plays a very important part in the study of interference, diffraction and quantum mechanics. The validity of this principle relies on the linearity of the mechanics and electromagnetism equations.
Our purpose in this chapter is to study the superposition of simple harmonic oscillations. The Fourier analysis considers any function as a superposition of simple harmonic functions. We study the case of periodic functions and of nonperiodic functions, namely signals of short duration.
2.1. Superposition of two scalar and isochronous simple harmonic oscillations
Consider the oscillations u1 = a1 cos(ωt + 1) and u2 = a2 cos(ωt + 2) that are scalar (or vectorial ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.