The length of time ( t ) in seconds it takes the pendulum of a clock to swing through one complete cycle is given by the formula t = 2 π √ l 32 where l is the length, in feet, of the pendulum, and π π is approximately 22/7 . how long must the pendulum be if one complete cycle takes 9 seconds? in feet

3.24 feet.

Step-by-step explanation:

We have been given that length of time ( T ) in seconds it takes the pendulum of a clock to swing through one complete cycle is given by the formula , where, L is the length, in feet, of the pendulum.

To find the length of pendulum, we will substitute in the given formula as:

Divide both sides by 2:

Substitute :

Multiply both sides by :

Square both sides:

Switch sides:

Therefore, the length of the pendulum is approximately 3.24 feet.

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.

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

L = 7.2012²

L = 51.88 feet

The simple pendulum should be 15.9 m long.

Step-by-step explanation:

Approximately (for small amplitudes), the period of a simple pendulum is

T = 2*pi * sqrt (L/g), L=length

using pi = 22/7, and g=9.8 m/s^2

8 = 2* 22/7 * sqrt(L/9.8)

solve for L

L = (8*7/(2*22))^2 * 9.8

= 15.874 m

That's quite a long pendulum!