What are the dependent, independent, and controlled variables of a simple pendulum?  

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Experiments are conducted to study the effect of change in a parameter on some other measurable parameter, while keeping other parameters in check. The parameter which is varied is the independent variable. The parameter which is measured and which changes as a result of change in the independent variable is the dependent variable. The parameter which is not allowed to vary is known as the controlled variable. 

In the experiment involving simple pendulum, we often study the effect of various parameters on the time period of the pendulum. The time period of the pendulum is given as:

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

Thus, we can think of the time period as the dependent variable. We often vary the length of the pendulum (L) in such experiments, and hence length of pendulum is the independent variable. We use the same setup, same material of string, same way of doing the experiment (same protocol), same altitude (so that value of g is same in all the experiments) and hence these all are controlled variables.

Note that in some experiments, effect of change in pendulum's mass is also studied and in those cases, mass of pendulum is also an independent variable.

Hope this helps.

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