Question

Where L is the length, in feet, of the pendulum, and π is approximately 22 7 . How long must the pendulum be if one complete cycle takes 8 seconds?

Answer 1

Length L = 51.88 feet

Explanation:

From the given information,

The length of the pendulum can be determined by using the Formula for the period T which is the time of one full oscillation of a simple pendulum.

`T = 2 \pi \sqrt {(L)/(g)}`

where;

T = period of the time of one full oscillation = 8 seconds

L = length in feet

g = acceleration due to gravity in feet = 32 ft/s²

π = 22/7

`8 = 2 * (22)/(7) * \sqrt {(L)/(32)}`

`8 = 6.2857 * \sqrt {(L)/(32)}`

`(8)/(6.2857) =\sqrt {(L)/(32)}`

`1.273=\sqrt {(L)/(32)}`

`1.273= {\frac{\sqrt L}{ \sqrt {32}}}`

`1.273 * { \sqrt {32}}}= {\sqrt L}`

`7.2012= {\sqrt L}`

L = 7.2012²

L = 51.88 feet