This paper on servomechanisms represents the first portion of a report by the author, printed December, 1941, by the Fire Control Committee of the N.D.R.C. It deals with the analysis by transient solution methods of the responses of several types of servomechanisms which are characterized by a servomotor load consisting principally of inertia and coulomb friction. A fairly complete discussion of the use of derivative- and integral-type controls is included, together with some discussion of the effect of response delays and limitations in torque.