The discussion revolves around a differential equation project, specifically focusing on maximizing the amplitude of the steady state solution for a given equation involving resistance (R), capacitance (C), and an unknown inductance (L). The equation provided is a second-order linear differential equation with a sinusoidal forcing function.
The discussion is active, with participants providing guidance on simplifying the problem and questioning the setup of the solutions. There is a recognition of potential mistakes in the original poster's approach, prompting further clarification on the definitions of steady state and transient solutions.
Participants note the importance of correctly identifying the components of the solution and the implications of the sinusoidal forcing function on the overall analysis. There is an emphasis on ensuring that all variables are appropriately handled in the context of the differential equation.
Instead of carrying the variables through all of your calculations, why don't you substitute in the values for R and C that you have? It would probably make your calculations easier.ZenPhys said:Homework Statement
This is for my differential equation project and this is the last part of the question.
We know that the R=2 and C=0.001. We are given the equation:
Q''+(R/L)Q'+(1/LC)Q=(117/L)sin(120*pi*t)
We want to find the value of L such that we maximize the amplitude of the steady state solution.
I have uploaded a document with my set-up so far and I appreciate any help at all!
What is your steady state solution? What is your transient solution? The general solution has a transient part (with the exponential terms) and a steady state part (caused by the forcing function).We want to find the value of L such that we maximize the amplitude of the steady state solution.