A simple pendulum oscillates, making four complete oscillations per second. The length of the pendulum is:
To calculate the length of a simple pendulum, we can use the formula for the period of oscillation, T:
T = 1/f
where T is the period in seconds and f is the frequency in hertz.
In this case, the pendulum completes four complete oscillations per second, which means the frequency is 4 Hz.
Therefore, the period of oscillation is:
T = 1/4 = 0.25 seconds
Now, we can use the formula for the period of a pendulum to find the length, L:
T = 2π√(L/g)
where L is the length of the pendulum and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Rearranging the equation to solve for L:
L = (T^2 * g) / (4π^2)
Substituting the values:
L = (0.25^2 * 9.8) / (4 * 3.1416^2)
Calculating:
L ≈ 0.096 meters or 9.6 centimeters
Therefore, the length of the pendulum is approximately 0.096 meters or 9.6 centimeters.