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Purposeful Distortion or It is Cool to be Square

The frequency Spectrum of a Sine Wave. (Click on the picture to expand it.)

Distortion is something that is unwanted in music reproduction systems. Those systems used to be advertised as high fidelity and claimed to reliably reproduce the sound files sent to them from phonograph records, audio tapes, etc. I have not heard

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Why both Sines and Cosines with the Fourier series?

Phase Shifting.

So far with the Fourier Series we have made some interesting waveforms but what happens in real life? Things are never as clean in real life as on paper. (Except maybe my smudged up papers.) If you think of a perfect square wave with an infinite number of odd harmonics, what would

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The Fourier Series — Part 1

A Fundamental and odd harmonics from 3 to 101

Tonight’s post is about adding multiple sine waves to create another waveform. Each of the sine waves is an positive integer (whole number) multiple of the frequency of the base sine wave. These additional frequencies are called harmonics of the the base frequency. The base

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The final analysis of a floating barrel. Flotation Part III

Bouyancy calcs for greater than 50% immersed.

Tonight’s post is the last of the posts about buoyancy and calculating the lift of a plastic barrel immersed in water. This shows the calculations for a barrel supporting a weight causing the barrel to be immersed greater that 50%.

The calculations are very similar to the

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The September Equinox and Look at what I just found!

Sine and Cosine waveforms.

Today is an equinox, a day of the year when the length of of time between sunrise to sunset is equal to the time between sunset to sunrise and the sun is directly overhead of the equator. Here in the northern hemisphere it is the autumn equinox and nights will

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A Plastic Barrel Pontoon Raft – Part 2

Breaking down the Problem into important areas.

This post and video is a continuation of the previous post. However, it is also much more. By calculating the lift of a partially submerged barrel we can estimate how high our raft will float in the water and how much we can load the raft. To

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Triangles, The Unit Circle and Radians

The Unit Circle andRadian Measurement of Angles

This is the last of the basic math posts for awhile. The next posts will be about creating a flotation platform that can be used as a raft or floating dock. We will be using much of this math. This one is based around a video like

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Vectoring in on a Solution – Phasors

Graphical representation of phase and amplitude.

Mathematics is really a bag of tricks to try to represent real and actions a provides a way to calculate and predict things. Over the next 2 or 3 posts I am going to arm you with a new set of tricks. However, it will be necessary to

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Circles and Cycles

Header

Sine and Cosine.

I created a video over the weekend showing the relationship of a sine wave to a cosine wave. The cosine wave is shifted 90 degrees from a sine wave. (Think Capacitors and Inductors!!! Deja Vu all over again!!!)

First, I create the two waveforms using the unit circle method and CAD.

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The impedance, Z, and Power triangles.

The Impedance Triangle.

Alternating current added a new complication to Ohms law. If we are working with only resistance, there is no problem as long as we use RMS values for volts and current. The math works great including the calculation for power. However, as soon as we added inductance or capacitance things started

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