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**1. Homework Statement**

A mass of density d floats in a liquid of density d_L. The mass is then pushed down a distance x and let go. Use Newton's Second Law to demonstrate that the mass will undergo simple harmonic motion. Recall that the SHM equation is d^2x/dt^2 + w^2*x = 0. Assume there is no friction. Find w in terms of whatever variables needed.

**2. Homework Equations**

**3. The Attempt at a Solution**

I know that Newton's 2nd law is sum F=ma, and Torque = I*omega. I don't see how I can relate this to simple harmonic motion, which involves things moving back and forth in the same pattern. The answer key says that w=SQRT(D_l * g/(D*H)). However, I don't know what I am missing to solve this problem. I don't know where to start.