Chapter Thirteen Notes - Chapter 13 Vibrations and Waves I...

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Chapter 13: Vibrations and Waves I) Periodic vibrations can cause disturbances that move through a medium in the form of waves II) Simple harmonic motion: when the net force along the direction of motion obeys Hooke’s law (F=-kx),  when the net force is proportional to the displacement from the equilibrium point and is always  directed toward the equilibrium point A) Amplitude (A): max distance of object from its equilibrium position.  In the absence of friction, an  object in simple harmonic motion oscillates b/t the positions x=-A and x=+A B) Period (T): time it takes the object to move through one complete cycle of motion  C) Frequency (f): number of compete cycles or vibrations per unit time, reciprocal of the period D) Harmonic oscillator equation: a=-kx/m (max value of x is the amplitude) III) Elastic potential energy: Energy stored in a stretched spring or some other elastic material A) a compressed spring has this and when allowed to expand, can do work on an object,  transforming spring potential energy into the object’s kinetic energy B) PE s ½  kx 2 IV) The total mechanical energy of the system consisting of the block and spring remains constant  A) (KE+PE g +PE s ) i =(KE+PE g +PE s ) f B) if nonconservative forces (friction) are present than W nc =(KE+PE g +PE s ) f- (KE+PE g +PE s ) i C) v= ±√ (k/m(A 2 -x 2 ) 1) Objects speed is at a maximum when x=0 2) Object’s speed is zero at x= ± A 3) Moving to the right is positive 4) Moving to the left is negative V) Comparing simple harmonic motion with uniform circular motion A) A/v o = (m/k) B) T=2 (m/k) π 1) Large mass means large period 2) Large spring constant yiels small period 3) Period does not depend on amplitude C) Angular frequency ( ): ω 1)   =2  f =  (k/m) ω
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