The time taken for a pendulum to complete one full oscillation (from one extreme to the other and back) is determined by its length and the acceleration due to gravity. The formula to calculate the period (time for one complete cycle) of a pendulum is:
T = 2π√(L/g)
where: T is the period of the pendulum, L is the length of the pendulum, and g is the acceleration due to gravity.
On Earth, the average value of the acceleration due to gravity is approximately 9.8 m/s².
Let's calculate the period of the pendulum first:
T = 2π√(L/g) T = 2π√(5.95m / 9.8 m/s²) T ≈ 2π√(0.6071) T ≈ 2π * 0.7788 T ≈ 4.894 seconds (approximately)
The period of the pendulum is approximately 4.894 seconds for one complete cycle.
Since the pendulum is allowed to oscillate through 5 cycles, we can calculate the total time it would take as follows:
Total time = T * number of cycles Total time = 4.894 seconds/cycle * 5 cycles Total time ≈ 24.47 seconds (approximately)
Therefore, if the pendulum with a length of 5.95 meters and an amplitude of 4.45 meters was on Earth, it would take approximately 24.47 seconds to complete 5 cycles of oscillation.