The theory of oscillations can be studied from a mathematical point of view in terms of
differential equations. The differential equation is written and then the solution or solutions
worked out and mathematically analysed. Provided physical, economic, social, or other
phenomena can be modelled in terms of equivalent differential equations, the solutions and
results are applicable to all phenomena all the same. On the other hand, it is sometimes easier
to learn a topic by having an experimental topic in mind. It is otherwise maybe surprising that
a large body of phenomena in many fields of application will be easily understood if the
equations are understood for a given case. The experimental analysis that forms the basis of
this book is cantilever dynamics in dynamic atomic force microscopy (AFM). In a nutshell,
the motion of the cantilever in dynamic AFM can be approximated to a perturbed driven
oscillator. The generality of the analysis presented here can be confirmed by noting that much
of what is covered in this book, particularly when dealing with the linear equation in section 1,
is similar to what is covered in generic expositions such as that by Tipler and Mosca1 or the
Feynmanβs lectures on physics2
. Maybe the main advantage of this exposition is that the linear
and nonlinear theories of oscillators, particularly phenomena that can be reduced to the analysis
of a point-mass on a spring, are discussed in detail and differences in terminology that could
lead to doubt, clarified. This means that this book can be used as a textbook to teach oscillation
theory with a focus on applications. This is possible because oscillations are present generally
in physics, engineering, biology, economics, sociology and so on. In summary, all phenomena
dealing with oscillations can be reduced, to a first approximation, to a restoring parameter, i.e.,
force in mechanics, following Hookeβs law
