I am not normally considered a member of the homework question supporter's club, but I did decide to answer Problem regarding Archimedes PrincipleProblem regarding Archimedes Principle, or at least provide a partial answer.
I think it's good that the Physics SE has an educational role. This doesn't mean answering all homework questions, but every now and then I see a question that I think many aspiring young physicists would benefit from. In this case the question was about a thinly disguised simple harmonic oscillator. Every physics student is going to encounter a dozen questions about thinly disguised SHOs, and it's important they know how to recognise and approach them. In principle the same may happen during a research career, though I must admit I can't remember ever having to model one of the systems I studied as an SHO.
The question is now closed, and I'm not complaining about that since it's blatantly homework. It also doesn't have a terribly helpful title so I doubt many aspiring young physicists will ever read it, let alone take away valuable lessons about simple harmonic oscillators. Nevertheless this is the sort of question where an answer can be helpful to many people, and I don't regret the time taken to answer it.