A Family of Transients Suitable for Reproduction on a Shaker Based on the cos^m(x) Window

A family of transients with the property that the initial and final acceleration, velocity, and displacement are all zero is derived. The transients are based on a relatively arbitrary function multiplied by window of the form cos^m(x). Several special cases are discussed which result in odd acceleration and displacement functions. This is desirable for shaker reproduction because the required positive and negative peak accelerations and displacements will be balanced. Another special case is discussed which will permit the development of transients with the first five (0-4) temporal moments specified. The transients are defined with three or four parameters that will allow sums of components to be found which will match a variety of shock response spectra.