The table of values shows the height of a pendulum from the floor over time as it swings back and forth in a simple harmonic motion. This can be modeled by a sinusoidal function.
Time (s) Height (cm)
Which statements are true?
Select each correct answer.
The period of the function is 5.4.
The frequency of the function is 1 .
The amplitude of the function is 0.4.
The period of the function is 1.
The period of a pendulum is the amount of time it takes a pendulum to complete one full cycle. One cycle would be the travel from one side to another, and then back to its starting position. Looking at the data we see that it completes a half cycle in 1 second. It goes from what we can imagine as the left side peak of 5.4 cm to a right side peak of 5.4 cm in 1 second. It would take 2 seconds to complete the movement back to its starting position. The period of the function is therefore 2 seconds. The frequency of a function is the inverse of the period, i.e.: period = seconds/cycle, frequency = cycles/second. If the period is 2 seconds, then the frequecy is 1/2 seconds-1. The only correct answer is the amplitude is 0.4 cm as the distance between the peak and rest positions is 5.4-5 = 0.4 cm.