Pendulum of the length L is suspended from the ceiling of an elevator. When the elevator is at rest , the period of the pendulum is T. In instant when the pendulum reaches its highest position the elevator starts the free fall. What is the period of the pendulum if the elevator is freely falling?

Are you asking the Period?
I believe it would remain at its peak until Impact.
Coolest Pendilum I have seen is at the Smithsonium, it knocks over a block every hour, you can tell time by it. I still have no Idea how that sucker works. Has to be a wobble, and be in sync with the hour?

The period of a pendulum is given by the formula:

T = 2\pi \sqrt{\frac{L}{g}}

pi is a constant and L is constant. When it is in free fall, what happens to the value of g?

Post what you think is the answer! :)

Coolest Pendilum I have seen is at the Smithsonium, it knocks over a block every hour, you can tell time by it. I still have no Idea how that sucker works. Has to be a wobble, and be in sync with the hour?

It's called a Foucault pendulum. It's inertia is such that it swings in a constant back and forth direction while the earth rotates beneath it. Hence to observers on the surface of the earth its swing appears to rotate. See: Foucault pendulum - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Foucault_pendulum)