Recent content by dawgs1236

Okay so ω=-λ working that out I came up with: ω1(t) = w1(0) cos -λt - [w2(0) + μ/λ] sin -λt ω2(t) = w1(0) sin -λt + [w2(0) + μ/λ] cos (-λt) - μ/λ

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...