ABSTRACT
This chapter presents numerical techniques for three classes of vibration problems; the single spring
mass, the multiple spring mass, and the continuous model. The simplest oscillatory problem results when
the problem can be modeled by the single spring-mass system. This system is modeled by a second-order
constant coefficient differential equation, which can be solved analytically when either there is no forcing,
or the forcing is harmonic. When the forcing is not harmonic, the finite difference method can be used to
solve this second-order equation or to solve the system of first-order equations, which is equivalent to the
second-order equation. A larger computational problem arises when there are multiple springs and
masses subjected to nonharmonic forcing. Again, the finite difference method can be used to compute
the full solution. It is not always necessary to compute the full solution. Often, all that is needed is
the fundamental frequency. This can be computed from the eigenvalues of a matrix problem. Both the
numerical solution to the full problem and the matrix problem will be discussed. Finally, one may want
to look at the vibration of a continuous element like a beam. Here, both the finite difference method and
the finite element method will be discussed.
