Period of a pendulum in a rotating coordinate system

[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.