{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Phys 0174 Fall 2008 - Chapter 15, 4 slides

# Phys 0174 Fall 2008 - Chapter 15, 4 slides - 1 Chapter 15...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 spring-mass 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 ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 7

Phys 0174 Fall 2008 - Chapter 15, 4 slides - 1 Chapter 15...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online