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1 VIBRATIONS AND WAVES Chapter 13 VIBRATIONS AND WAVES circle6 Waves carry (propagate) energy circle6 Waves on a string circle6 Light waves circle6 Waves are related to oscillations circle6 So we begin by looking first at simple oscillatory motion Simple Harmonic Motion (I) circle6 Specific type of periodic motion circle6 Simple Harmonic Motion (SHM) circle6 Due to Hooke’s law. F s = - kx circle6 x = displacement from equilibrium circle6 k is the spring constant. (Determined by the stiffness of the spring) circle6 The further away the system is from equilibrium, the stronger the force F s = - k x circle6 Resulting motion is described by a sine or cosine curve i.e. harmonic functions circle6 SHM is periodic, but there are periodic motions that are not SHM
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2 Simple Harmonic Motion (II) circle6 x = 0 is equilibrium position circle6 Pull the mass to maximum amplitude x = A circle6 With no friction present, the mass will continue to oscillate between x = ± A circle6 Period of oscillation is T circle6 Frequency of oscillation is f = 1/T circle6 Units are: Hz = cycles/sec Newton’ 2 nd Law and SHM circle6 From Newton’s second law we have: F = - kx = ma circle6 Therefore a = - kx / m circle6
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