Some First-Passage Problems in Random Vibration

First-passage problems for a lightly damped linear oscillator excited by white noise are described for two types of initial conditions and three different types of barrier configurations. The qualitative behavior of the probability distribution of the time to first passage is discussed. Two numerical procedures utilizing high-speed digital computers are outlined, and quantitative results for first-passage probability densities are displayed. The asymptotic behavior of this density for long mean times to failure is discussed, and a table of experimentally determined mean times to failure is included.