TweetWe’ll begin with a square function, f(t), that has a an amplitude of 1, a start time of 2 seconds and an end time of 4 seconds. Next, a time shift is demonstrated. Here our function is changed from f(t) to f(t-2). Notice that subtracting 2 from t in the function results in a positive [...]
Tags: amplitude, duration, function, graph, scale, shift, signal, time
Posted by Jeff on Dec 30, 2009 in
Differential Equations,
Linear Systems
TweetWhy do we need to solve system equations? 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: [...]
Tags: complex roots, Differential Equations, linear system equation, Linear Systems, solve for complex roots, system equation, system equations
Posted by Jeff on Sep 25, 2009 in
Zero-Input Response
TweetCharacterizing the zero-input response 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, [...]
Tags: Characteristic Modes, Characteristic Roots, Initial Conditions, RLC, Series RLC, Zero-Input Response, ZIR
TweetWhat is the Laplace Transform method? 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 [...]
Tags: laplace, laplace method, laplace table, laplace transform, laplace transform examples, laplace transforms, table of laplace transforms
