A simple harmonic pendulum has a period of 3.19 s and initial speed of 2.12 m/s. Find the length.

To find the length of a simple harmonic pendulum, we can use the equation for the period of a simple pendulum:

T = 2π√(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

In this case, we are given the period T = 3.19 s. Speed is not directly relevant in this situation, so we do not need to consider the initial speed of 2.12 m/s.

Rearranging the equation, we have:

L = (T^2 * g) / (4π^2)

Let's substitute the given values into the equation to find the length L:

L = (3.19^2 * 9.8) / (4π^2)

L ≈ 8.044 m

Therefore, the length of the simple harmonic pendulum is approximately 8.044 meters.