Hi, first time asking questions in this forum.
I am self-learning classic mechanics this summer using Laudau's book and so far I feel everything is pretty interesting and makes sense for me. But still, I have some questions that needed to be answered. One of them is about the parametric resonance.
The equation of motion is x'' +ω2（1+h*cosγt）*x = 0, and I am told that the resonance reaches its maximum when γ is close to 2ω,i.e. γ = 2ω+ε. To find out the solution for x, the author assumes the solution to be in the form of x = a(t)cos(ω+1/2ε)+b(t)sin(ω+1/2ε)， I don't quite understand how the author comes up with this assumption. Really appreciated if someone can help me.
I am self-learning classic mechanics this summer using Laudau's book and so far I feel everything is pretty interesting and makes sense for me. But still, I have some questions that needed to be answered. One of them is about the parametric resonance.
The equation of motion is x'' +ω2（1+h*cosγt）*x = 0, and I am told that the resonance reaches its maximum when γ is close to 2ω,i.e. γ = 2ω+ε. To find out the solution for x, the author assumes the solution to be in the form of x = a(t)cos(ω+1/2ε)+b(t)sin(ω+1/2ε)， I don't quite understand how the author comes up with this assumption. Really appreciated if someone can help me.