Measuring Acceleration due to Gravity: The Period of a Pendulum

We are asked to find g given the period T and the length L of a pendulum. We can solve $T=2\pi \sqrt{\frac{L}{g}}$ for g, assuming that the angle of deflection is less than 15 degrees. Recall that when the angle of deflection is less than 15 degrees, the pendulum is considered to be in simple harmonic motion, allowing us to use this equation.

1. Square $T=2\pi \sqrt{\frac{L}{g}}$ and solve for g.
   $$g=4{\pi }^2\frac{L}{T^2}$$
2. Substitute known values into the new equation.
   $$g=4{\pi }^2\frac{0.75000\text{ m}}{{(1.7357\text{ s})}^2}$$
3. Calculate to find g.
   $$g=9.8281\text{ m}/{\text{s}}^2$$