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
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:
Multiply both sides by :
Square both sides:
Therefore, the length of the pendulum is approximately 3.24 feet.
Length L = 51.88 feet
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 = 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.
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!