Exploration of the Laplace Transform
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The author designed a Physics lab using the Laplace Transformation to be used in Dr. Tom Askew’s Physics 370 class. The Laplace Transform gives us another option when it comes to solving differential equations. In short, we are able to convert a differential equation (in the time domain, t) into an algebraic equation (in the frequency domain, s), solve for our solution, then convert back into the time domain. This is very useful for those who do not have a strong background in calculus, differential equations, and/or complex numbers as the process is pretty straight forward. This method also allows us to solve differential equations that have step and periodic forcing functions. Finally, it is important to note that the math gets messy pretty quickly when using this method, so it is nice to have a computer algebra software, such as Maxima, as an aide.