A reference frame attached to the earth

A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limit $$ - \phi $$ and $$ + \phi $$. For an angular displacement $$\theta $$ $$\left( {\left| \theta \right| < \phi } \right)$$, the tension in the string and the velocity of the bob are T and V respectively. The following relations hold good under the above conditions:

In the arrangement shown in Fig. the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed.
Mass M moves upwards with a speed