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A pendulum refers to a mass suspended from a point around which it is free to swing. The length of the pendulum is the distance of the mass from the fixed point or pivot.
For a pendulum with length l, the time period is given by the equation `T = 2*pi*sqrt(l/g)` , where g refers to the acceleration due to gravity at the point where the pendulum is located. The time period of the pendulum is dependent only on the length of the pendulum and the gravitational acceleration, it is independent of the mass of the pendulum.
The period of a pendulum can be changed either by varying the length of the pendulum or moving the pendulum to a location where the value of acceleration due to gravity is different. The value of g decreases as height increases. To change the period of a pendulum without changing its length, it would have to be taken further away from ground level. An increase in altitude would increase the time period. The time period of a pendulum increases constantly as it is taken to a higher altitude. How high one would need to take a pendulum to notice a change in the period is dependent on the accuracy of the instruments being used to make the measurements.
It is not clear what you mean by "change in height," when you have asked for how much of a change in that will change the period of the pendulum. Change in height could mean increasing or decreasing the length of the pendulum, it could also mean actually taking the pendulum to a higher point from ground level. The period of the pendulum is changed when either of these is done. The difference in period will change for every change in the length of the pendulum or a change in its height. For example, if a person living on the beach were to take a pendulum clock to a house located top of a mountain they would have to adjust the pendulum slightly.
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