Period of a Mathematical Pendulum

In a pendulum, the period (T) is dependent on the mass (M), the length of the wire (L), and the gravity acceleration (G) that acts on the mass. We presume some relationships T = a, b, c are undetermined exponents. Now the dimension 

In a more complicated situation, the following method is good form the derivatives with respect to kg, m, and s. Equate the resulting equations at kg = m = s = 1. This method is suitable for a symbolic calculator and subsequently a session with the program DERIVE(r) [29] is given that does the job for the above example. 

The alert reader will observe that chemical equations can be balanced with a similar method. 

In principle, it is allowed to use arbitrary units, even general units such as L for a length. 

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