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.
Practical resonance is the phenomenon where an object or system vibrates at its natural frequency when exposed to an external force. It is important because it can cause significant damage or failure in mechanical systems, and understanding and controlling it is crucial in engineering and design.
The natural frequency of a system can be determined by conducting a frequency response analysis, using a vibration analyzer, or by performing experiments and measuring the response of the system to various frequencies.
The stiffness, mass, and damping of the system, as well as the frequency and amplitude of the external force, can all affect practical resonance. Other factors such as temperature, material properties, and environmental conditions may also play a role.
To minimize the effects of practical resonance, you can adjust the stiffness, mass, and damping of the system, or change the frequency and amplitude of the external force. Using materials with different properties or implementing isolation techniques can also help reduce the impact of practical resonance.
Yes, numerical simulations can be used to predict practical resonance by modeling the system and analyzing its response to different frequencies. However, experimental validation is still necessary to ensure the accuracy of the simulations.