The discussion focuses on solving the second order differential equation y'' + y = cos(wt) with the general solution y(t) = a cos(t) + b sin(t) + (cos(wt)/(1 - w^2)). The key objective is to determine the time it takes for the solution to approach the steady state solution. Participants emphasize the importance of correctly interpreting the steady state solution and the homogeneous solution, highlighting the need for precise mathematical notation in expressions.
PREREQUISITESStudents and educators in mathematics, particularly those focusing on differential equations, as well as engineers and physicists applying these concepts in practical scenarios.
The good news is that you are being very diligent in your use of parentheses, but the bad news is that some of them aren't in the right place. You should write the last expression above as cos(wt)/(1 - w^2). As you have it, this expression would be read as cos(wt)/1 - (w^2), or cos(wt) - w^2, and I'm pretty sure that's not what you intended.freeski said:Homework Statement
if given the general solution to a differential equation
y(t)=a cos t + b sin t + ((cos wt)/1-w^2),
A good start would be to find out what the term "steady state solution" means.freeski said:Find out how long it takes the solution to approach the steady state solution.
original second order differential equation:
y'' + y = cos wt such that 0 < w < 10
Homework Equations
The Attempt at a Solution
I am not sure where to begin.