The discussion revolves around a differential equation of the form X" + X = 2Asin(t - 8), where participants are exploring the methods to find particular and general solutions. The context involves a new research lab, with the original poster expressing uncertainty about how to approach the problem.
Some participants have provided insights into the structure of the solutions and methods to approach the problem. There is an ongoing exploration of different solution forms, and the original poster seeks further clarification on the reasoning behind these suggestions.
The original poster indicates a lack of familiarity with the topic, having received the lab assignment as an assistant. There is an implication of needing foundational knowledge in differential equations, particularly those with constant coefficients.
Shandra2 said:Homework Statement
X" + X = 2Asin (t - 8)
Homework Equations
The Attempt at a Solution
I don't really even know where to begin. I got this lab as just an assistant and it's just something they were talking about and I'm not really sure how to start.
hunt_mat said:You have you particular solution and your general solution. The general solution is trhe solution of [tex]\ddot{x}+x=0[/tex] and I would look for a particular solution of the form:
[tex] x_{p}=\alpha\cos (t-8)+\beta\sin (t-8)[/tex]
The solution will be the sum of your particular and general solutions.
Shandra2 said:Can you explain to me how you get there? I appreciate you taking the time on something which isn't really that serious. I just want to understand this more.