In any experiment, the variables are classified as either control, independent or dependent. Control variables are those that are to changed and hence controlled. Independent variables are those that are changed and we study the effect of changes in these variables. Dependent variables are those that are affected by changes in independent variables.

For a simple pendulum, we commonly study the time period and experiment with various variables that might affect it. The time period of a simple pendulum is given as:

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

where, T is time period, L is the length of pendulum and g is the acceleration due to gravity. The time period, thus, depends on length of the pendulum.

Even though the time period of pendulum does not depend on the mass of pendulum bob, it is often used as a variable.

Since, length of pendulum and mass of bob are both changed, one at a time, in experiments on simple pendulum, they are both independent variables. Thus **option C** is correct.

Hope this helps.

The period T of a single pendulum is given by the formula:

T =2pi sqrt(l/g)

Thus we see that the period only depends on the length of the pendulum. It does not depend on the initial angle of displacement of the bob. Nor does it depend on the mass of the bob.

By the way measuring the period of a simple pendulum by timing 20 swings and taking an average provides a convenient way of measuring g, the acceleration due to gravity. By manipulation T^2 = 4pi^2(l/g)

Thus g = 4pi^2(l/T^2)

The period of a spring depends on the mass of the object at the end of the spring. The formula for the period of a spring is T = 2pi sqrt (m/k).

To sum up the independent variable for a simple pendulum is its length and the independent variable for a spring is it is mass.

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