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Physics 218 Chapter 18

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Title: New Phenomena: Recent Results and Prospects from the Fermilab Tevatron Author: toback Last modified by: Rupak Mahapatra Created Date: 2/16/2000 4:53:28 AM – PowerPoint PPT presentation

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Title: Physics 218 Chapter 18


1
Physics 218Chapter 18
  • Prof. Rupak Mahapatra

2
Chapter 18 Periodic Motion
  • This time
  • Oscillations and vibrations
  • Why do we care?
  • Equations of motion
  • Simplest example Springs
  • Simple Harmonic Motion
  • Next time
  • Energy


Concepts

?The math
3
(No Transcript)
4
What is an Oscillation?
  • The good news is that this is just a fancy term
    for stuff you already know. Its an extension of
    rotational motion
  • Stuff that just goes back and forth over and over
    again
  • Stuff that goes around and around
  • Anything which is Periodic
  • Same as vibration
  • No new physics

5
Examples
  • Lots of stuff Vibrates or Oscillates
  • Radio Waves
  • Guitar Strings
  • Atoms
  • Clocks, etc
  • In some sense, the Moon oscillates around the
    Earth

6
Why do we care?
  • Lots of engineering problems are oscillation
    problems
  • Buildings vibrating in the wind
  • Motors vibrating when running
  • Solids vibrating when struck
  • Earthquakes

7
Whats Next
  • First well model oscillations with a mass on a
    spring
  • Youll see why we do this later
  • Then well talk about what happens as a function
    of time
  • Then well calculate the equation of motion using
    the math

8
Simplest Example Springs
  • What happens if we attach a mass to a spring
    sitting on a table at its equilibrium point
  • (I.e., x 0) and let go?
  • What happens if we attach a mass, then stretch
    the spring, and then let go?

9
Questions
  • What are the forces?
  • Hookes Law F -kx
  • Does this equation describe our motion?
  • x x0 v0t ½at2

10
The forces
No force
Force in x direction
Force in x direction
11
More Detail
Time
12
Some Terms
Amplitude Max distance Period Time it takes
to get back to here
13
Overview of the Motion
  • It will move back and forth on the table as the
    spring stretches and contracts
  • At the end points its velocity is zero
  • At the center its speed is a maximum

14
Simple Harmonic Motion
  • Call this type of motion
  • Simple Harmonic Motion
  • (Kinda looks like a sine wave)
  • Next The equations of motion
  • Use SF ma -kx
  • (Here comes the math. Its important that you
    know how to reproduce what Im going to do next)

15
Equation of Motion
  • A block of mass m is attached to a spring of
    constant k on a flat, frictionless surface
  • What is the equation of motion?

16
Summary Equation of Motion
  • Mass m on a spring with spring constant k
  • x A sin(wt f)
  • Where
  • w2 k/m
  • A is the Amplitude
  • is the phase
  • (phase just allows us to set t0 when we want)

17
Simple Harmonic Motion
  • At some level sinusoidal motion is the definition
    of Simple Harmonic Motion
  • A system that undergoes simple harmonic motion
  • is called a
  • simple harmonic oscillator

18
Understanding Phase Initial Conditions
  • A block with mass m is attached to the end of a
    spring, with spring constant k. The spring is
    stretched a distance D and let go at t0
  • What is the position of the mass at all times?
  • Where does the maximum speed occur?
  • What is the maximum speed?

19
Check
  • This looks like a cosine. Makes sense

Spring and Mass Paper which tells us what happens
as a function of time
20
Example Spring with a Push
  • We have a spring system
  • Spring constant K
  • Mass M
  • Initial position X0
  • Initial Velocity V0
  • Find the position at all times

21
What is MOST IMPORTANT?
  • Simple Harmonic Motion
  • X A sin(wt f)
  • What is the amplitude?
  • What is the phase?
  • What is the angular frequency?
  • What is the velocity at the end points?
  • What is the velocity at the middle?
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