The period of a pendulum can be found by using the formula,where L is length of the pendulum in feet and P is the period in seconds.Find the period of a 15-foot pendulum. Round your answer to the nearest hundreth of a second.
T^2 = 4*pi^2(L/g).
T^2 = 9.87(15/32) = 4.63
T = 2.15 s.
To find the period of a pendulum using the given formula, you need to substitute the length of the pendulum into the equation.
The formula is given as:
P = 2π * √(L/g)
Where P is the period in seconds, L is the length of the pendulum in feet, and g is the acceleration due to gravity which is approximately 32.2 feet per second squared.
By substituting the length of the pendulum, L = 15 feet, into the formula we get:
P = 2π * √(15/32.2)
To calculate this, you'll need a calculator. Follow these steps:
1. Divide 15 by 32.2:
(15 / 32.2) = 0.465
2. Take the square root of the result:
√0.465 ≈ 0.682
3. Multiply the square root by 2π (approximately 6.283):
0.682 * 6.283 ≈ 4.283
Rounding your answer to the nearest hundredth of a second, the period of the 15-foot pendulum is approximately 4.28 seconds.