ABSTRACT
When a dynamical system is excited by a suddenly applied non-periodic excitation F(t), the response to such excitation is called transient response, since steady-state oscillations are generally not produced. Such oscillations take place at the natural frequencies of the system with the amplitude varying in a manner dependent on the type of excitation. This chapter discusses the response of a spring-mass system to an impulse excitation because this case is important in the understanding of the more general problem of transients. The Laplace transform method of solving the differential equation provides a complete solution, yielding both transient and forced vibrations. When the differential equation cannot be integrated in closed form, numerical methods must be employed. The Runge-Kutta computation procedure is popular because it is self-starting and results in good accuracy. In the Runge-Kutta method, the second-order differential equation is first reduced to two first-order equations.
