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

Answer:

Length L = 51.88 feet

Step-by-step 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.

$T = 2 \pi \sqrt {\dfrac{L}{g}}$

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

$8 = 2 \times \dfrac{22}{7} \times \sqrt {\dfrac{L}{32}}$

$8 = 6.2857 \times \sqrt {\dfrac{L}{32}}$

$\dfrac{8}{6.2857} =\sqrt {\dfrac{L}{32}}$

$1.273=\sqrt {\dfrac{L}{32}}$

$1.273= {\dfrac{\sqrt L}{ \sqrt {32}}}$

$1.273 \times { \sqrt {32}}}= {\sqrt L}$

$7.2012= {\sqrt L}$

L = 7.2012²

L = 51.88 feet