The present paper is concerned with the determination of the frequency equation and sensitivity of the eigenfrequencies of a fixed-free longitudinally vibrating rod carrying a tip mass to which a spring-mass system is attached in-span. First, the exact frequency equation is established, and then an approximate formula is given for the fundamental frequency, based on Dunkerley's procedure. Moreover, using the normal mode method, a second approximate but very accurate frequency equation is established with the help of which a sensitivity formula is derived later. Frequency equations of some simpler systems are also obtained from the general expressions by using limiting processes. These novel equations can be very useful for a design engineer who is interested in the eigencharacteristics of similar systems, and their sensitivity. (C) 1998 Academic Press.