What is the length of a simple pendulum, which has a frequency of 0.5 Hz (take g = 10 m/s²)?

The time period (T) of a simple pendulum is given by the formula:
T = 2π√(L/g)
The frequency (f) is the reciprocal of the time period (f = 1/T), so:
f = (1/2π) × √(g/L)

Given:
Frequency (f) = 0.5 Hz
Acceleration due to gravity (g) = 10 m/s²

Substituting the values into the formula:
0.5 = (1/2π) × √(10/L)
Multiplying both sides by 2π:
π = √(10/L)
Squaring both sides:
π² = 10/L
L = 10/π²

Using the approximation π² ≈ 9.87 (often taken as 10 in physics problems where g = 10 m/s² for simplification):
L ≈ 10/10 = 1 m

A pendulum with a frequency of 0.5 Hz has a time period of 2 seconds, which is known as a "seconds pendulum." Its length is approximately 1 meter.