When the lift accelerates upwards at a rate w, it is equivalent to the situation where acceleration due to gravity were g+w instead of g. The time period of the pendulum in the upward accelerating lift is given by,
Since the time period of the pendulum under normal conditions should be,
during the time when the elevator is accelerating upwards, the clock runs faster (since the time period as given by (1) is smaller) by a factor .
When the list accelerates downwards at a rate w, it is equivalent to the situation where the acceleration due to gravity is g-w. The time period of the pendulum when the list is accelerating downwards is given by,
Thus, during the time when the elevator is accelerating downwards, the clock runs slower (since the time period as given by (2) is longer) by a factor .
The time required by the list to travel a height h starting from rest while accelerating at a rate w is given by,
The time shown by the clock at the end of this interval is going to be,
Now let us assume that the elevator travels downwards for a time duration before the clock shows the correct time. The corresponding time duration as seen in the downward accelerating clock will be given by,
For the time to be correct, at the end of then,
The total time the elevator traveled is then given by,