This paper investigates the control challenges posed by non-collocated mechatronic systems and motivates the need for a model-based control technique towards such systems. A novel way of implicit constraint handling by online penalty adaptation (PAMPC) is proposed which enables the computation of the MPC transfer function and thus the usage of linear system tools for analysis. The PAMPC is shown to be of particular relevance towards control of underdamped, non-collocated systems by exploiting the structure of such systems. The controller is demonstrated on a benchmark mass-spring-damper system, which poses all the mentioned challenges.