Question

A pendulum close to the surface of the earth oscillates with a period of 3.76 seconds. How long is the pendulum?

Answer 1

We can find the length of the pendulum from the formula:

$$T = 2 \pi \sqrt{\dfrac{L}{g}},$$

here, $T = 3.76 \ s$ is the period of the pendulum. $L$ is the length of the pendulum and $g = 9.8 \ \dfrac{m}{s^2}$ is the acceleration due to gravity.

Then, from this formula we can find the length of the pendulum:

$$L = \dfrac{T^2 g}{4 \pi^2} = \dfrac{(3.76 \ s)^2 \cdot 9.8 \ \dfrac{m}{s^2}}{4 \pi^2} = 3.51 \ m.$$

Answer:

$L = 3.51 \ m.$