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1. Discrete Fourier Transform of Sine Function

(1) For a real function, g(x), the Fourier integral transform is defined by g(x) = \int_{0}^{\infty} A(\omega )cos(2\pi \omega x)d\omega - \int_{0}^{\infty} B(\omega )sin(2\pi \omega x)d\omega where A(\omega ) = 2 \int_{-\infty}^{\infty} g(x)cos(2\pi \omega x)dx and B(\omega ) = 2...
2. Parabolic Two-Body Motion

I have been working with elliptical motion for a while, so am aware that when one body revolves around another in an elliptical orbit it sweeps out equal areas in equal times (measured from a focus). However, I am not sure if the same applies to parabolic motion. If, say, a comet approaches...
3. Help Solving a Quartic Polynomial

I am trying to solve an equation: arccos(Y) = arctan(Y), where Y = 1/x This turns into a quartic equation: x4 - x2 - 1 = 0 It looks simple enough to simplify further; however, I must be having a brain-fart because I can't do it. I'd like to avoid resorting to a numerical solution...
4. Simplify Condition for Chord Length Equals Angle?

Consider the following: On a circle of radius 1, two points are marked: P1 and P2. Two lines are drawn from the center of the circle: one from the center to P1, the other from the center to P2. The angle between these two lines is \theta. One more line is drawn: from P1 directly...
5. Root-finding Algorithm Question

Some time ago I saw a thread in which was mentioned a root-finding algorithm that converges twice as fast as the Newton-Raphson method. Newton-Raphson converges to a zero at a quadratic rate, and a poster pointed out that another algorithm converges to a zero at a quartic rate. I have tried...
6. Angular Momentum of Moving Water?

A spinning top has angular momentum that creates a force that keeps it from falling over, and it precesses. Mass in motion has momentum and/or angular momentum. That made me wonder: Does fluid in motion create angular momentum? If so, how would it materialize? Consider a fictional...
7. Online Bookmarking Site for Students

I recently came across a bookmarking site aimed at students: http://www.brainify.com/" [Broken] It is not specifically for Math, Physics, and Engineering students, but students in general. To sign up for an account, users need to use a college or university email address. There are...
8. Wireless Electricity

I came across an interesting story today and thought I would share it here. http://www.fastcompany.com/magazine/132/brilliant.html" [Broken] Neat stuff. Although I do wonder, even if they get it working and feasible for large-scale adoption, would there be any adverse health affects? (I...
9. Physics of a Water Pendulum

Hi, folks. I am looking for some help to understand the physics of a water pendulum (in fact, I don’t even know if my terminology is correct). It has been several years since I left school and my math/physics tools are rusty. Here’s the set up: Whenever I come back from the beach with a...