This paper presents an analysis of the first passage time problem. A lumped-parameter model for a structural system is considered, and the excitation is limited to white noise. The response of this type of system is a Markov process on a multidimensional position-velocity space (for a damped harmonic oscillator the position-velocity space is two-dimensional). The Markov property is used to develop an integral equation for the first passage time-density function. Numerical results are presented for the damped harmonic oscillator. A rest start condition is considered, i.e., position and velocity are zero, and symmetric position boundaries are considered for the region of safe operation.

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