  Hereditary effects of exponentially damped oscillators with past histories
are considered in this paper. Nonviscously damped oscillators involve
hereditary damping forces which depend on time-histories of vibrating motions
via convolution integrals over exponentially decaying functions. As a result,
this kind of oscillators are said to have memory. In this work, initialization
for nonviscously damped oscillators is firstly proposed. Unlike the classical
viscously damped ones, information of the past history of response velocity is
necessary to fully determine the dynamic behaviors of nonviscously damped
oscillators. Then, initialization response of exponentially damped oscillators
is obtained to characterize the hereditary effects on the dynamic response. At
last, stability of initialization response is proved and the hereditary effects
are shown to gradually recede with increasing of time.
