Question

What is the length of a pendulum that has a period of 4. 89 seconds?

Answer 1

Hi there!

We can use the following equation for a simple pendulum:

$T = 2\pi \sqrt{\frac{L}{g}}$

T = Period (4.89 s)
L = length (? m)
g = acceleration due to gravity (9.8 m/s²)

Rearrange the equation to solve for L.

$T^2 = 4\pi ^2 \frac{L}{g}\\\\L = \frac{gT^2}{4\pi ^2}$

$L = \frac{(9.8)(4.89^2)}{4\pi^2} = \boxed{5.936 \frac{m}{s}}$