Find the length of a pendulum that oscillates with a frequency of 0.19 Hz

To find the length of a pendulum that oscillates with a frequency of 0.19 Hz, we can use the formula for the period of a pendulum. The period (T) is the time taken for one complete oscillation. It is the inverse of the frequency (f).

The formula for the period of a pendulum is:
T = 1/f

In this case, the frequency (f) is 0.19 Hz. Substitute this value into the formula to find the period (T):
T = 1/0.19

Calculating this value, we get:
T ≈ 5.26 seconds

The period (T) is the time taken for one complete oscillation. For a pendulum, one complete oscillation consists of swinging back and forth from one side to the other and then returning to the original side. So, the period is the time it takes to complete one full swing.

However, the length of the pendulum is not directly given, and we need to use an additional equation to find it. The formula for the period (T) of a simple pendulum is:

T = 2π√(L/g)

Where:
T = Period
L = Length of the pendulum
g = Acceleration due to gravity

In this case, we are trying to find the length of the pendulum. Rearranging the formula, we get:

L = (T^2 * g) / (4π^2)

Substituting the known values, we can calculate the length (L) of the pendulum:

L = (5.26^2 * 9.8) / (4 * π^2)

Simplifying the calculation, we get:

L ≈ 1.43 meters

Therefore, the length of the pendulum that oscillates with a frequency of 0.19 Hz is approximately 1.43 meters.