Dimensional Analysis of a Pendulum

We begin by listing in Table 5.5 the physical quantities that describe a pendulum. We also assign a mnemonic symbol to each quantity and list each quantity s dimensions. 

Why does amplitude have no dimensions Recall that amplitude is an angle measured in radians. The amplitude of an angle is the ratio of the length of a radius divided by the arc swept out by the radius. The dimensions of amplitude are thus L/L, which is dimensionless. 

Have we neglected anything How about the viscosity of the medium through which the pendulum moves This would be important, for example, in designing an underwater pendulum. We neglect it for now. 

We wish to use a small model of a pendulum to predict the period of oscillation, 

This function must be dimensionally consistent. Whatever combination of parameters we derive for the right side of Eq. (5.10), each term must have dimensions of time, T. That is, the function we seek will have some general form 

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