Question

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.Which statements are true?

Answer 1

From the table, we can say that the highest point is 5.4 and the lowest point is 5

Note that the amplitude is half of the difference between the highest point and the lowest point.

This will be :

$\frac{1}{2}(5.4-5)=0.2$

The amplitude is 0.2

Period is the measurement of one complete cycle.

From the table, we can say that from t = 0, the height is 5 and t = 1, the height is also 5.

So we can conclude that within 1 sec, the pendulum will complete one cycle.

The period is 1

The frequency is the number of period in 1 cycle.

The formula is :

$\text{frequency}=\frac{1}{\text{period}}$

This will be :

$\text{frequency}=\frac{1}{1}=1$

Therefore, the frequency is 1

The answers are :

The period of the function is 1

and

The frequency of the function is 1