Foucault's Pendulum and Inertial Oscillation

Everyone understand?

If you swung Foucault's Pendulum at the North Pole, the axis of oscillation would make one rotation a day. However, the period of inertial oscillation at the North Pole is a half day. When I was a student, I couldn't understand why it works out that way. If you solve the equation, a half day is the answer you get for the period of inertial oscillation, but why?

I asked a lot of people and received many different answers, but what it came down to was that "if you solve the equation, that's the answer you get".

I only realized years later that if you make the cycle of the pendulum one day, then from the point of view of the earth, the cycle would be half that.

Does everyone really understand, though?