Question

What length pendulum would have a period of 1.00 seconds?

Please show all steps including all of the algebra used to get to the answer.

Answer 1

The time period of a simple pendulum is given as:

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

where L is the length of the pendulum and g is acceleration due to gravity = 9.81 m/s²

Given, T = 1 s

$\small 1= 2\pi \sqrt{\frac{L}{g}}$

$\small 1^2= 4\pi^2 {\frac{L}{g}}$

$\small L = {\frac{g}{4\pi^2 }} = {\frac{9.81}{4\pi^2 }} = 0.24 m$