The paper examines the lateral vibrations of a system with a pendulum suspension. It is assumed that the system consists of a rigid body elastically connected to the trolley frames. In turn, the frames can rotate around a longitudinal axis passing through the centers of gravity of the parts of the trolleys on which the springs are installed. At the same time, vertical movements of trolley frames and lateral movements of the body relative to the frames are also not excluded from consideration. To construct periodic solutions to the resulting system of nonlinear equations, we will use the averaging method in its special form, which was proposed by Bulgakov for quasilinear systems. The influence of liquid (linear) friction of dampers on body vibrations is considered. This type of friction is a special case of Coulomb friction, when instead of the nonlinear signum function, the linear dependence of the force on the speed of movement is considered. Equations have been determined that must be used when studying the vibrations of a system with a pendulum suspension in the presence of a dry friction damper.