- #1

- 2

- 0

For a coupled two-body oscillator we write the general solution as:

x1(t)=C1

_{-}Cos[ω

_{-}t+ψ

_{1-}]+C1

_{+}Cos[ω

_{+}t+ψ

_{1+}]

x2(t)=C2

_{-}Cos[ω

_{-}t+ψ

_{2-}]+C2

_{+}Cos[ω

_{+}t+ψ

_{2+}]

Where we determine C1

_{-}/C2

_{-}and C1

_{+}/C2

_{+}from the normal mode condition.

We call ψ

_{1-}=ψ

_{2-}=ψ

_{-}and ψ

_{1+}= ψ

_{2+}=ψ

_{+}, and we end up with 4 adjustable constants: C1

_{-},C1

_{+}, ψ

_{-}, ψ

_{+}.

Why is that? Why can't ψ

_{2-}be a function of ψ

_{1-},( ψ

_{1+}maybe), C1

_{-}and C1

_{+}, such that ψ

_{2-}(C1

_{+}=0)=ψ

_{1-}, in order to keep the "pure", in phase, normal mode solution? The same for ψ

_{2+}.

Thank you in advance!