In the limit as t goes to infinity the solution approaches
where K and t0 depend on ω (note: t0 = t subscript 0)
I am attempting to show that K(ω) = 1/(ω^4-ω^2+1)^1/2 and failing
I believe that at t=0. The only important part of the general solution to the original equation is the exponential part (because e^0=1while as t increases (and eventually to the limit) only the particular solution is of importance
hence i have tried equating Ksin[ω(t-t0)] with the particular solution and failing.
The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore, ...
The solution shows how to solve the damped driven harmonic oscillator equation and how to writethe solution as a single sine wave with a constant phase.