Question

Overview: As discussed in the video and demonstration in class, the course project involves mod- eling and analyzing the system dynamics of a tall building during an earthquake, and minimizing the vibration by designing a tuned mass damper control system Description: In project module 1, you will do the dynamic modeling to obtain the equations of motion for an active mass damper system based on the general schematic below. The schematic represents a tall building that resists swaying with a structural spring constant ki and damping coefficient bi. The ground motion x,t) is considered an external input to the system due to an earthquake. At the top of the building there is a reaction mass connected to the building by a spring and damper, which we will tune later in the project. Assume the wheel is massless and rolls without friction. To complete the design, we first need the coupled differential equations that govern the motion of the building and the reaction mass (described 2, and 22). Deliverables: Submit a complete and well-organized derivation dard form, using either a Newtonian or Lagrangian approach. You may discuss with others, but only submit your own work. An acceptable model for discussion is to work through the problem in a group on a whiteboard, then crase the board, and write up your solutions individually. I will be available during office hours to assist as needed. Submit a hard copy of your work in class on 2/20/2020. Reaction Mass Building Mass m m Moving Platform

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Answer 1

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