T is the time period of simple pendulum on the earth's surface. Its time period becomes $$x$$ T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of $$x$$ will be :

The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $$\alpha$$, is given by :

Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth surface. Clock - 1 and Clock - 2 operate at time periods 4 s and 6 s respectively. Then the value of h is -

(consider radius of earth $$R_{E}=6400 \mathrm{~km}$$ and $$\mathrm{g}$$ on earth $$10 \mathrm{~m} / \mathrm{s}^{2}$$ )

When a particle executes Simple Hormonic Motion, the nature of graph of velocity as a function of displacement will be :