A wooden block of cross-sectional area A, height h, and density 蟻_1 floats partially submerged in a fluid of density 蟻_2. If the block is displaced downward and then released, it will oscillate with simple harmonic motion. Find the period of its motion.
What equations would you use for this problem, and what is your strategy of solving the problem?|||Simple harmonic motion arises when there is a restoring force which is proportional to displacement, so F = kx. With a spring, that k is the spring constant. With a pendulum, it is a term which is related to the gravitational force on the swinging mass.
Whatever the constant k represents, when you have such a force, the period is 2*pi*sqrt(k/m).
In this case, the constant is going to be derived from the buoyancy force. The more you submerge, the more volume of water you displace. The force will be the weight of the displaced water. Work out what that is in terms of displacement x.
Hint: If you submerge the block by vertical distance x, you displace a volume of A * x of water.
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