The period of a simple pendulum is 3.5 s. The length of the pendulum is doubled. What is the period T of the longer pendulum?

Question

asked Oct 15, 2022 90.4k views

1 Answer

Anho · Answer 1 · 2022-10-21T22:10:58+0000

Step-by-step explanation:

The period T of a simple pendulum is given by

$T = 2 \pi \sqrt{(l)/(g)}$

Doubling the length of the pendulum gives us a new period T'

$T' = 2 \pi \sqrt{(l')/(g)} = 2 \pi \sqrt{(2l)/(g)}$

$\:\:\:\:\:\:\:= √(2) \left(2 \pi \sqrt{(l)/(g)} \right)$

$\:\:\:\:\:\:\:= √(2)\:T = √(2)(3.5\:\text{s})= 4.95\:\text{s}$