# Chapter 15 - Exercises and Problems - Page 281: 68

The proof is below.

#### Work Step by Step

We know that the force on the pencil is: $F= -\rho_{water}gax$ We apply Newton's second law to find: $m\frac{dx^2}{dt^2}=-\rho_{water}gax$ (Recall, $\frac{dx^2}{dt^2}$ equals acceleration.) We also know the following equations: $\omega = \sqrt{\frac{g}{L}}$ $T=\frac{2\pi}{\omega}$ Combining these three equations, we find: $T = 2\pi\sqrt{\frac{L}{g}}$

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