Final answer:
The given statement is false. The pendulum does not swing 2.3 feet in both directions and complete one full cycle every 6 seconds. The time period of a pendulum can be calculated using the formula T = 2π√(L/g).
Step-by-step explanation:
The given statement is false. A pendulum swings back and forth in an oscillatory motion. The distance it swings in each direction is called the amplitude of the pendulum. The period of a pendulum is the time it takes to complete one full cycle of its motion. The time period(T) of a pendulum is given by the formula:
T = 2π√(L/g)
Where:
T = Time period
L = Length of the pendulum
g = Acceleration due to gravity
Based on the given information, we can calculate the time period of the pendulum using the formula T = 6 seconds and L = 2.3 feet:
T = 2π√(L/g)
6 = 2π√(2.3/g)
√(2.3/g) = 6/(2π)
2.3/g = (6/(2π))²
g = (2.3/(6/(2π))²)
g ≈ 20.76 ft/s²
Therefore, the given statement is false and the acceleration due to gravity required for a pendulum to complete one cycle in 6 seconds with an amplitude of 2.3 feet is approximately 20.76 ft/s².