ABSTRACT
Many times throughout this volume, we have encountered problems concerning the dynamics of mass particles. In the Newtonian theory, the second law of motion requires the acceleration of a particle with a fixed mass m to be proportional to the resultant force acting on the particle: y ** = F/m. (A dot indicates a derivative with respect to time in this and the next chapter.) More than one kind of force may act on the particle. In a mass-spring and dashpot system, the mass is subjected to the restoring force of the spring − ky and the frictional force of the dashpot − cy *. If the system is affected by the gravity field of the Earth, the gravitational force − mg must also be considered. The oscillation of the mass may also be driven by time-varying forces supplied externally by motors or other mechanical or electrical devices and summarized by Fm (t). The resulting vertical acceleration of the (lumped) mass of this system is given by () y * * = − c m y * − k m y − g + 1 m F m ( t ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203749821/5a9bd1b0-aa97-4dfe-adb3-8f69a65a6308/content/eq3406.tif"/>
