Question

A pendulum on earth oscillates with a period of 3.45 seconds. What is the length of the pendulum?

Answer 1

Answer:

The length of the pendulum is 2.954 m.

Explanation:

Given;

period of the pendulum, T = 3.45 s

The period of the pendulum oscillation is given as;

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

where;

L is length of the pendulum

g is acceleration due to gravity on Earth = 9.8 m/s²

$l = \frac{gT^2}{4\pi ^2}\\\\l = \frac{(9.8)(3.45)^2}{4\pi ^2}\\\\l = 2.954 \ m$

Therefore, the length of the pendulum is 2.954 m.