Generally, we carry out experiments to study the quantitative effects of changing the length of the pendulum and mass of the bob, on the time period of an oscillating pendulum. The time period of an oscillating pendulum is given as:
`T = 2pisqrt(L/g)`
As we can see from this relationship, the time period is a function of length of the pendulum and has no relation to the mass of the bob. If we change the length of the pendulum by a factor of 4, the new time period of the pendulum will be twice (= `sqrt 4 = 2` ) the original time period. If we reduce the pendulum length by a factor of 4, that is the new length is 25% of the original length, the time period would be only half of the original value. In comparison, any changes in the mass of the bob will have no effect on the time period of an oscillating pendulum.
Hope this helps.
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