The formula used to determine frequency (f) in vibrations of a pendulum given its length (L) in meters and the acceleration due to gravity (g) in meters per second squared is:

f = (1/2π)√(g/L)

where:

- π (pi) is a constant approximately equal to 3.14159

- f is the frequency of the pendulum in vibrations per second (Hertz)

- g is the acceleration due to gravity (approximately 9.8 meters per second squared on Earth)

- L is the length of the pendulum in meters

To use this formula, simply substitute the values of L and g into the formula and calculate the result. The answer will be the frequency of the pendulum's vibrations in Hertz.

For example, if the pendulum has a length of 1 meter and is on Earth, the formula would be:

f = (1/2π)√(9.8/1) ≈ 0.5 Hz

This means that the pendulum will oscillate back and forth (complete one vibration) approximately 0.5 times per second.