This article presents an application of standard undergraduate ODE techniques to a modern engineering problem, that of using a tuned mass damper to control the vibration of a skyscraper. This material can be used in any ODE course in which the students have been familiarized with basic spring-mass models, resonance, and linear systems of ODEs. Indeed, the problem can be used to motivate why one cares about spring-mass models, or numerical solutions to ODEs. Many suggested problems are included; most require the use of a symbolic and numerical ODE solver with graphical capabilities. (Contains 5 figures.)