Transcription of Chapter 4 Oscillatory Motion
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Chapter 4 Oscillatory Motion
Chapter 4 Oscillatory The Important Simple Harmonic MotionIn this Chapter we consider systems which have a Motion whichrepeats itself in time, that is,it isperiodic. In particular we look at systems which have some coordinate(say,x) whichhas a sinusoidal dependence on time. A graph this kind of Motion is shown inFig. Suppose a particle has a periodic, sinusoidal Motion on thexaxis, and its motiontakes it betweenx= +Aandx= A. Then the general expression forx(t) isx(t) =Acos( t+ )( )Ais called theamplitudeof the Motion . For reasons which will become clearer later, iscalled theangular frequency. We say that a mass which has a Motion of the type givenin Eq. undergoessimple harmonic we see that when the timetincreases by an amount2 , the argument of thecosine increases by 2 and the value ofxwill be the same.
72 CHAPTER 4. OSCILLATORY MOTION m m (a) (b) (c) x Figure 4.3: (a) Unstretched vertical spring of force constant k (assumed massless). (b) Mass attached to spring is at equilibrium when the spring has been extended by a distance mg/k.
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