Chapter 12Oscillations
Chapter 12 Oscillations
Mechanical oscillations:pendulum, string of a guitar, vocal cords, ..More general oscillations:Electrical, optical, atomic, ...Oscillations: motions that repeat themselvesAn object moves back and forth repeatedly aroundthe equilibrium positionOr a physical quantity changes repeatedly arounda fixed value
Mechanical oscillations: pendulum, string of a guitar, vocal cords, . More general oscillations: Electrical, optical, atomic, . Oscillations: motions that repeat themselves An object moves back and forth repeatedly around the equilibrium position. Or a physical quantity changes repeatedly around a fixed value
Analysis ofoscillationsSimple harmonic motion (SHM) is the mostsimple and basic oscillation.Every oscillation can be composed of SHMR
Analysis of oscillations Simple harmonic motion (SHM) is the most simple and basic oscillation. Every oscillation can be composed of SHM
Oscillations of a springHorizontal Spring-mass systemF=-kx(Hooke's law )1-D motion, origin o is the equilibrium positionx is the displacement of the object relative to oF is called restoring forceF<0x>0: stretched.00000000mx<0: compressed, F>0x=0+xm-Xm
Oscillations of a spring Horizontal Spring-mass system F kx = − 1-D motion, origin o is the equilibrium position x is the displacement of the object relative to o F is called restoring force x>0: stretched, F<0 x<0: compressed, F >0 ( Hooke’s law )
Dynamic equation of SHMAny vibrating system with a restoring forceF=-kxexhibits a simple harmonic motion (SHM)d2xd?x+0'x=0mkxdt?dt?where m is the mass which is oscillating0=/k/mangular frequencyThis is called the dynamic equation of SHM
Dynamic equation of SHM 2 2 d x m kx dt = − Any vibrating system with a restoring force F kx = − exhibits a simple harmonic motion (SHM) 2 2 2 0 d x x dt + = where m is the mass which is oscillating = k m/ This is called the dynamic equation of SHM angular frequency