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Unformatted text preview: 1 Chapter 15 Oscillations ¾ Displacement, velocity and acceleration of a simple harmonic oscillator ¾ Energy of a simple harmonic oscillator ¾ Examples of simple harmonic oscillators: ¾ springmass system ¾ simple pendulum ¾ physical pendulum ¾ torsion pendulum ¾ Damped harmonic oscillator ¾ Forced oscillations/Resonance 2 Figure a shows snapshots of a s Simple Harmoni imple oscillati c Motion ( ng system SHM) . The motion is periodic which means it repeats in time. The time needed to complete one cycle is known as the The number of cycles per unit time ( perio is ca symbol , u lled the d fr nits: s). equen s cy ( T ymbol , unit hertz). f 1 f T = 3 ( ) The displacement of the particle is given by the equation: Figure b is a plot of ( ) versus . The quantity is called the of the motion and it is the maximum possible ( ) cos . amplitude d m m x t x t x t t x ω φ = + angular isplacem frequenc ent of the oscillating object. The quantity is called the of the oscillator and it is given by the equation: y 2 . f ω ω π = 2 2 f T π ω π = = ( ) ( ) cos m x t x t ω φ = + 4 ( ) ( ) cos m x t x t ω φ = + The quantity is called the of the oscillator. The value of is determined from the displacement (0) and the velocity (0) at 0. In figure a, ( ) is plotted versus ph for 0. ase ang ( le ) x v t x t t x t φ φ φ = = cos m x t ω = ( ) ( ) Velocity of SHM ( ) ( ) cos sin m m dx t d v t x t x t dt dt ω φ ω ω φ = = + = − + The quantity is called the It expresses the maximum possible value of ( ). In figure b, the velocity ( velocity amplitu ) is plotted versus for 0. de . m m x v t v t t v ω φ = ( ) sin m v t x t ω ω = − 5 2 The quantity is called the . It expresses the maximum possible value of a( ). In figure c, the acceleration a( ) acceleration amplitude is plotted versus for a ....
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 Spring '10
 Cohen
 Physics, Acceleration, Energy, Simple Harmonic Motion, Ω, xm cos

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