Determine the length of a pendulum that has a period of 4 seconds.
To determine the length of a pendulum that has a period of 4 seconds, you can use the formula for the period of a simple pendulum:
T = 2π √(L/g)
Where:
- T is the period of the pendulum (in seconds)
- L is the length of the pendulum (in meters)
- g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)
To solve for L, we rearrange the formula:
L = (T/2π)² * g
Now, substitute the given values into the formula:
T = 4 seconds
g = 9.8 m/s²
L = (4/2π)² * 9.8
Calculating this expression will give us the length of the pendulum.
To determine the length of a pendulum with a period of 4 seconds, you can use the formula for the period of a pendulum:
T = 2π√(L/g)
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.8 m/s²).
Rearranging the formula to solve for L:
L = (T/(2π))^2 * g
Substituting T = 4 seconds and g = 9.8 m/s²:
L = (4/(2π))^2 * 9.8
L = (2/π)^2 * 9.8
L = (4/π^2) * 9.8
L ≈ 0.395 * 9.8
L ≈ 3.9 m
Therefore, the length of the pendulum is approximately 3.9 meters.