It depends on the mass (m), specific heat (c), convective heat transfer coefficient (h) and the surface area (As)
In other words,
Time Constant = (m * c) / ( h * As)
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The time of a period doesn't depend on the mass of the Bob(that'll be a mass spring system) It also doesn't depend on Friction..
Dependent upon the variables, you need to take into consideration factors that can affect the outcome of the result; what will make the result vary in any way. If this, for example, entails the variable to be kept constant time, you will monitor the time and repeat it throughout the experiment. This is my understanding of constant variables; hope this helped.
It does depend on the force of gravity where the pendulum is located. There are other factors that it depends on but their contribution, in normal circumstances, is negligible enough to ignore.
Ordinary constant is a real constant which is same in all time but arbitrary constant is not constant at all time intervals, especially we can see arbitrary constants in integrals.For example the anti derivative of x+C is 1. Here we can replace C with any constant so C is arbitrary constant
Tropic of Cancer is approximately 231/2oN and the Tropic of Capricorn is approximately 231/2oS. (Their exact positions vary over time as they depend on the tilt of the earth which is not constant but varies.)