“At what frequencies does a mechanical system vibrate at resonance?”
When a system vibrates at its resonance there could be numerous deleterious consequences such as structural rupture. As a result engineers often want to find out the Modal Frequencies (also known as natural frequencies) of a system.
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“What happens when we have a matrix where everything outside of the diagonal is zero?”
Matrices come in all shapes and sizes. But some of them are very special indeed. One of these include matrices where everything outside of the main diagonal is zero. These very special easy to solve matrices are known as Diagonal Matrices and are great for solving equations.
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Row Echelon Form
“How can we simplify matrices to solve them?”
Solving matrices is one of the most fundamental parts of modern day science and engineering. But how can we put it into a form where it’s easy to solve? Well, we could take the top row, make sure that all entries under the leading column are zero, and then repeat the process until we are at the end. Putting a matrix in this form is known as Row Echelon Form, and is one of the most common ways to solve Linear Algebra problems.
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The Difference Between Probability and Statistics
“What is the difference between Probability and Statistics?”
In everyday talk, probability and statistics are lumped together. But in reality they are more like two sides of the same coin. Probability is the prediction of the likelihood of future events while Statistics is the analysis of the frequency of past events. Therefore, this is The Difference Between Probability and Statistics.
Why Planar Lines With the Same Slope Never Meet
“Why is is that lines in a plane with the same slope never meet?”
Lines in a plane usually intersect at some point. But with one exception. If the lines have the same slope, then they will never meet! This is because they are parallel to each other and planar parallel lines never meet.
Quasi-static Time Series
“How can we work with time-dependent and discrete data?”
Distributed Energy Resources can have many different discrete processes that are time dependent such as solar panels producing usable current and batteries absorbing energy. And sometimes these time-dependent processes might actually have multiple different time periods. Since normal analysis is too difficult to integrate with this, we can use something called Quasi-static Time Series to quantify our data.
“Does solar power price drops have some form of pattern?”
Every day it seems that we hear about the price drop of solar power. However, does this price change somehow have a pattern? Well, a solar industrialist known as Richard Swanson was analyzing the data and found that PV module prices drop 20 percent for every doubling of cumulative shipped volume. This phenomenon is known as Swanson’s law and is similar to Moore’s law in Computer Science.