I was solving a classic application of Archimedes' principle: a body partially submerged that is made to oscillate vertically and perform a simple harmonic oscillations. The equations turn out to be the right ones for a sho but then it struck me: How is it that the liquid remains static? The body is moving vertically and the liquid should be affected.
Is this an approximation? Because I've seen this "problem" in many lecture notes. If so, how can I strictly justify the approximation? Does Buoyant force=rho gV still hold exactly?