The formula t = 2 pi startroot startfraction l over 32 endfraction endroot relates the time, t, in seconds for a pendulum with t

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The formula t = 2 pi startroot startfraction l over 32 endfraction endroot relates the time, t, in seconds for a pendulum with t

he length, l, in feet, to make one full swing back and forth. what is the length of a pendulum that makes one full swing in 2.2 seconds? use 3.14 for pi. 2 feet 4 feet 11 feet 19 feet

Mathematics

1 answer:

natita [175] · Answer 1 · 2023-08-09T06:09:14+03:00

The length of this pendulum that makes one full swing is 3.93 meters.

<h3>How to calculate the length of the pendulum?</h3>

Mathematically, the time taken by this pendulum is given by this formula:

$\rm T=2\pi \sqrt{\dfrac{L}{32}}$

Making L the subject of the formula, we have:

$\rm T=2\pi \sqrt{\dfrac{L}{32}}\\\\32T^2=4\pi ^2L\\\\L=\dfrac{32T^2}{4\pi ^2}\\\\$

Substitute all the values in the formula

$\rm L=\dfrac{32T^2}{4\pi ^2}\\\\ L = \dfrac{32 \times 2.2^2}{4 \times 3.14 ^2\\}\\\\ L =\dfrac{154.88}{39.43}\\\\L=3.93 \ m$

Hence, the length of this pendulum that makes one full swing is 3.93 meters.