Sunday, December 4, 2016

What will cause an increase in the period of a simple pendulum that is swinging with small amplitude?

The time period of a simple pendulum which is oscillating is given by the following equation:


`T = 2pi sqrt(L/g)`


where, T is the time period of oscillations, L is its length and g is the acceleration due to gravity. 


Thus, the time period is directly proportional to the square root of the pendulum length. That is,


`T alpha sqrtL`


This means that in order to increase the time period of a simple pendulum, we have to increase its length. If the length of the pendulum is increased by a factor of 4, the time period increases by a factor of 2. 


That is, `T' alpha sqrt(L')`


`T' alpha sqrt(4L)`


`T' alpha 2sqrt(L)`


`T' = 2T`


The change in the mass of a pendulum will not have any effect on the time period of the pendulum. 


Thus, pendulum length is the only variable on which the time period of a simple pendulum depends.


Hope this helps.

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