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Unformatted text preview: Chapter 15 Oscillations In this chapter we will cover the following topics: Simple harmonic oscillator: Displacement, velocity, acceleration, kinetic and potential energy. Examples of simple harmonic oscillators: springmass system, simple pendulum, physical pendulum, torsion pendulum Damped harmonic oscillator Forced oscillations/Resonance (151) In fig.a we show snapshots of a simple oscillating system. Simple Harmonic Motion (SHM) The motion is periodic, i.e. it repeats in time. The time needed to complete one repetition is the The number of repetitions per u (symb nit t ol , unit ime is th s s). (symbol , unit e T f period frequency ( 29 The displacement of the particle is given by (see Fig.b). is called the of the SHM. It gives the maximum displacement of the oscillating object is cal h l er 1 ( ) c tz ed th . ) os = = + m m f T x x t x t amplitude e of the SHM. It is given by the equation: angular frequency (152) ( 29 ( ) cos m x t x t = + 2 2 f T = =x m x m O ( 29 ( ) cos m x t x t = + ( 29 ( 29 ( 29 ( 29 The quantity is called the . The value of is determined from (0) cos and the velocity (0) sin at 0. ( ) ( ) cos sin The quantity = =  = = = + =  + = Velocity of SHM m m m m m x x v x t dx t d v t x t x t dt dt v phase angle is called the It expresses the maximum valu e of ( ) m x v t velocity amplitude ( 29 ( 29 2 2 2 ( ) ( ) sin cos The quantity is called the . It expresses the maximum value of a( ). = = + =  + =  = Acceleration of SHM m m m m dv t d a t x t x t x dt dt a x t acceleration amplitude (153) 2 a x =  = ( 29 ( 29 = + m x t x cost Simple Harmonic Motion (contd) cos( t) cos( t /4) cos( t+ /4) ? m m x x' T T ' /4 15.2.1. Object A is attached to ideal spring A and is moving in simple harmonic motion. Object B is attached to ideal spring B and is moving in simple harmonic motion. The period and the amplitude of object B are both two times the corresponding values for object A. How do the maximum speeds of the two objects compare? a) The maximum speed of A is one fourth that of object B. b) The maximum speed of A is one half that of object B. c) The maximum speed of A is the same as that of object B. d) The maximum speed of A is two times that of object B. e) The maximum speed of A is four times that of object B. 15.2.1. Object A is attached to ideal spring A and is moving in simple harmonic motion. Object B is attached to ideal spring B and is moving in simple harmonic motion. The period and the amplitude of object B are both two times the corresponding values for object A. How do the maximum speeds of the two objects compare?...
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This note was uploaded on 09/27/2010 for the course PHY 55555 taught by Professor Ia during the Spring '10 term at SUNY Buffalo.
 Spring '10
 IA

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