Chapter 11. Elasticity and Periodic motionPowerPoint PresentationSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Circle of ReferenceSlide 17Slide 18Slide 19Slide 20Energy in SHMSlide 22Energy conservation in SHMSlide 24Slide 25X versus t for SHO then simple variations on a themeSlide 27Slide 28SUMMARYChapter 11. Elasticity and Periodic motionStress and strainHook’s law: stress/strain=constant0/VVpBBulk modulus(Shear modulus for steel 0.84 ·10^11Pa)N02)/(llStrainmNAFStress(No dimension)or (Pa)Simple harmonic motion SMHSimple harmonic motion is the projection of uniform circular motion on a diameter.Consider a ball on a circular track on the table and looking at it from the sideCircle of Referencex = A Cos(t + ) v = - A Sin(t + ) = = 2 f 2T-a=- 2 A Cos(t + )A force varying with distance is the basis of SHMEnergy in SHMEnergy in SHM•Energy is conserved during SHM and the forms (potential and kinetic) interconvert as the position of the object in motion changes.E 12mvx212kx212kA212mvmax2Energy conservation in SHMF = -mg Sin -mg x = L F - x mgLF = -kx k = mgL = max Cos(t + )km = =gLNote: mass doesn’t enter amplitude doesn’t enterX versus t for SHO then simple variations on a themex(t) Acos(t )VERY IMPORTANT: frequency and period of oscillations DO NOT depend on the amplitude!!What is the period of a pendulum on mars (g(mass)=3.71 m/s^2), if the period of this pendulum on earth is 1.6 sec.SUMMARYPeriodic motion: motion that repeats itself in a defined cycle.f 1TT 1f2f 2TSimple harmonic motion: if the restoring force is proportional to the distance from equilibrium, the motion will be of the SHM type. The angular frequency and period do not depend on the amplitude of oscillation.Fx kx axFxmkmxkmf 212kmT 2mkx Ac os(t )Energy in SHM:E 12mvx212kx212kA212mvmax2Simple pendulum:gLf 12gLT
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