Engineering can be difficult. Let's make it a little easier, shall we?
Often during a course you will need to be able to solve a system equation for its roots. These roots can be complex, distinct, or repeated. These problems usually arise when working with linear systems or differential equations. A system equation is formatted as follows:
System Equation:
For example purposes, I will solve a system equation [...]
The total response of a given system can be expressed as the sum of two components: the zero-input component and the zero-state component:
Total response = zero-input response + zero-state response.
Our system:
Where represents our input and represents our output.
The zero-input response, which we will be solving for here, is the system response when [...]
The Laplace Transform is a method that simplifies integral and differential equations into algebraic equations. This practice is commonly used to solve for a function out of a differential equation, which otherwise may have been unsolvable or very difficult. The following integrals can be used to transform between where denotes Laplace and [...]
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Jeff Schuler