Chapter 5Bessel Functions
The important role that trigonometric and hyperbolic functions play in the study of oscillations is well known. The equation of motion of a uniform rigid rod of length 
suspended from one end and oscillating freely in a plane is given as 
where 
is the moment of inertia, 
is the mass, 
is the acceleration of gravity, and 
is the angular displacement of the rod from its equilibrium position. For small oscillations, using the approximation 
we obtain the general solution in terms of trigonometric functions as
Suppose the rod is oscillating inside a viscous fluid exerting a drag force proportional to with the proportionality constant as the drag coefficient. Now ...
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