I did just guess at that.
okay so I set up the characteristic equation and got sqrt(λ) as the answer. would that make it:
ω1(t) = A sin sqrt(λ)t + B cos sqrt(λ)t + C ?
Would it be a good idea to take the second derivative of :
ω2(t) = D sin ωt + E cos ωt
and plug them them into:
ω2¨ = -λ^2ω2 +λμ
and then use the initial conditions?
Obviously I know they're wrong. Why else would I post this here? I posted it here looking for help with the solution not conformation that I was incorrect.
So does μ affect this problem?
the answers I came up with were
ω_{1}(t) = ω_{2}(0) sin ωt + ω_{1}(0) cos ωt
ω_{2}(t) = ω_{1}(0) sin ωt + ω_{2}(0) cos ωt
but these were wrong
Yeah I know how to do that part. I'm really just not sure what to do about the μ on the end. When I take the derivative it should disappear but I don't think it should.
Homework Statement
\dot{ω_{1}} = λω_{2} +μ
\dot{ω_{2}} = -λω_{1}
Homework Equations
λ and μ are real, positive constants
ω_{1}(0) ≠ 0
ω_{2}(0) ≠ 0
The Attempt at a Solution
I know that the general solution will be in the form
ω1(t) = A sin ωt + B cos ωt + C
ω2(t) = D sin...