Question

When a weight is tied on the end of a string and is pulled back and released, it creates a pendulum. The time it takes for the pendulum to swing out and return to its original position is called the period, and depends on the length of the string.

For small release angles, like the one in the video, we can use the equation T = 2πWhen a weight is tied on the end of a string and is pulled back and released, it creates a pendulum. The time it takes for the pendulum to swing out and return to its original position is called the period, and depends on the length of the string.
For small release angles, like the one in the video, we can use the equation T = 2π√L/g, where

T is the period of the swing, in seconds
L is the length of the string, in meters
g is gravity, about 9.8 m/s²

My stopwatch estimated the period to be 1.28 seconds. Use this to determine the length of the string, in meters, to at least 3 decimal places

Answer 1

The length of the string of the pendulum with a period of 1.28 seconds is approximately 0.416 meters, calculated using the formula T = 2π√(L/g).

Step-by-step explanation:

To determine the length of the string (L) of a pendulum given the period (T), we can rearrange the formula T = 2π√(L/g) and solve for L. Given that the period T is 1.28 seconds and the acceleration due to gravity (g) is approximately 9.8 m/s², we can calculate the length L as follows:

L = (T / (2π))² * g

Substituting the values into the equation:

L = (1.28 / (2 * 3.14159))² * 9.8 ≈ 0.416 meters.

The calculated length of the string with three decimal places is 0.416 meters.