Relation of the period of a pendulum

[ataglance05]

Homework Statement

What is the formula that relates the period of a pendulum on a rotating coordinate system to the angular velocity of the coordinate system? (assume pendulum is in a gravitational field that produces an acceleration equal to the gravitational acceleration on Earth's surface)

 

[Mentz114]

Under form rules, you should share your thoughts and show what you've done yourself.

 

[m2003]

The formula that relates the period of a pendulum on a rotating coordinate system to the angular velocity of the coordinate system is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. This formula is known as the "small angle approximation" and is valid when the angle of displacement of the pendulum is small. In a rotating coordinate system, the angular velocity would need to be taken into account in the calculation of the period, as it would affect the motion of the pendulum. This formula assumes that the pendulum is in a gravitational field that produces an acceleration equal to the gravitational acceleration on Earth's surface. If the gravitational acceleration is different, the formula would need to be modified accordingly.