This work is concerned with disturbance amplification in interconnected systems which contain a large number of elements. The main focus is on passive control of a chain of masses where a single point is subject to an external disturbance. This problem arises in the design of multi-storey buildings subjected to earthquakes, but applies in other situations such as bidirectional control of vehicle platoons. We investigate the "scalability" of this system, i.e., the ability to control a system behaviour independent of its size. It is shown that the scalar transfer functions from the disturbance to a given intermass displacement can be represented as complex iterative maps. Using these expressions, the H-infinity norm of these transfer functions is shown to be uniformly bounded for certain choices of interconnection impedance. Graphical approaches to select a suitable interconnection impedance are proposed both for the case when the length of the mass chain is known and unknown.