Question

Students are observing the effects of increasing and decreasing the length of a pendulum’s string on the pendulum’s period. The period of a pendulum is one back-and-forth swing. The function P(L) = 1.11√L gives the period P (in seconds) of a pendulum as a function of the length L (in feet) of the pendulum's string.

How many times greater is the length of a pendulum string that has a period of 2.72 seconds than the length of a pendulum string that has a period of 2.22 seconds?
Enter the correct solution in the box. Round your answer to the nearest tenth

Answer 1

The ratio of the lengths of two pendulum strings with different periods can be calculated using the given function. The ratio when rounded to the nearest tenth is approximately 1.1.

Step-by-step explanation:

The period of a simple pendulum is given by the function P(L) = 1.11√L, where P is the period in seconds and L is the length of the pendulum's string in feet.

To find the ratio of the lengths of two pendulum strings with periods of 2.72 seconds and 2.22 seconds, we can calculate:

Ratio of lengths = Length with period 2.72 seconds / Length with period 2.22 seconds

Plugging in the values, we get:

Ratio of lengths = 1.11√(2.72) / 1.11√(2.22)

Rounding to the nearest tenth, the ratio of the lengths is approximately 1.1.