Nature of motion of a pendulum Consider a pendulum suspended from the ceiling of a lift in free fall ,
if its displaced from its mean position , what will be its nature of motion?
what i thought was that it would simply stick to the ceiling as the lift's in free fall;
but on the contrary what my teacher said was that ,
as
  "g" = 0 it's  time period  will be "infinity".   

Thus it implies it won't move at all.
But is that even possible?
please provide me with some reason or correct me if I'm wrong.
any help appreciated.
cheers.
 A: Your teacher is right. It is an experimental fact that being in free-fall is indistinguishable from being in the complete absence of gravitational fields. For instance, consider an astronaut aboard a satellite orbiting the Earth. We've seen videos; the astronauts appear completely weightless. But note that there's still gravity where they are! Satellites are not out in deep space, they're rather close to the Earth, and the effects of gravity are still relatively strong. The reason they seem weightless is because they are in a state of perpetual free-fall. That is to say, all satellites are constantly falling to Earth; the reason they don't reach the surface is because they all have a horizontal/tangential velocity, though this is besides the point.
The point then, is that your lift in free-fall would behave precisely like a lift in deep space. You wouldn't expect a pendulum to be pulled towards the ceiling in deep space, and so you shouldn't expect a pendulum to be pulled towards the ceiling in free-fall!
To look at this from a more classical perspective, note that gravity is a unique force in that it is proportional to the mass of the body on which it acts. Because the acceleration of an object is equal to the force acting on it divided by its mass, we find that the acceleration of an object under gravity is independent of its mass --- this was one of the discoveries of Galileo Galilei, I believe.
What this means is that all objects in our lift --- including the lift itself --- fall towards the Earth with the same acceleration. This means that if the relative motions of the objects in the lift are zero at one instance of time, their relative positions will remain fixed for all future time. So if you displaced the pendulum from the vertical by some angle and let it go, the distance from the bob of the pendulum to the ceiling wouldn't change.
If that distance were to change, the accelerations of the ceiling and the bob of the pendulum would have to differ. If the pendulum were to fly up and hit the ceiling, that would mean that the ceiling was accelerating faster than the pendulum. But as we've established, the lift and the pendulum fall at the same rate --- that's gravity!
$$F_\mathrm{gravity} = mg \,, \qquad F = ma \,, \quad \implies \quad a = g = 9.8 \,\mathrm{ms}^{-2
} $$
