Page - 147 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

4.3 OscillatingOne-DimensionalSystems 147 Fig.4.29 Excitation force that causes resonance 4.3.11 Spring-MassSystemwithSlidingFriction Abodywithmassm isattached toaspringwithstiffnesskwhile slidingonaplane surface. Thebodyisalsosubject toafrictionforcef.u0/duetothecontactbetween the bodyand theplane. Figure4.30depicts the situation. The friction forcef.u0/ canbemodeledbyCoulombfriction: f.u0/D 8 <ˆ :ˆ mg; u0 <0; mg; u0 >0; 0; u0 D0 where is the frictioncoefficient, andmg is thenormal forceon thesurfacewhere the body slides. This formula can also bewritten asf.u0/ D mgsign.u0/, pro- Fig.4.30 Sketchofaone-dimensional, oscillatingdynamic systemsubject toslidingfrictionand aspring force