Mechanical Scaling: Lumped Element Modelling

This lecture introduces the concept of Lumped Element Modelling (LEM) in mechanical systems, simplifying complex systems into discrete elements that exchange energy. The lecture covers the equations of motion for a mass connected to a spring and damper, the modeling of complex springs, and the representation of a complex deformation as a simple spring. It also discusses the modeling of a simple cantilever and the use of lumped-parameter modeling in mechanics to reduce mechanical structures to mass-spring models. Additionally, it explores the exact analytical calculation of natural frequencies, the electrical equivalent circuit, and the generalized variables in different cases.

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File:LC parallel simple.svg|LC circuit diagram File:Low cost DCF77 receiver.jpg|LC circuit ''(left)'' consisting of ferrite coil and capacitor used as a tuned circuit in the receiver for a [[radio clock]] File:Tuned circuit of shortwave radio transmitter from 1938.jpg|Output tuned circuit of [[shortwave]] [[radio transmitter]] An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together.