9.1 clocks new ideas for today resonance harmonic oscillators timekeeping
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9.1 Clocks9.1 Clocks
New ideas for todayNew ideas for today• Resonance• Harmonic oscillators• Timekeeping
•~3500 BC: sundials•~1500 BC: water clocks
History of timekeepingHistory of timekeeping
Earliest clocks: EgyptEarliest clocks: Egypt
Modern timekeepingModern timekeeping•1500-1510: spring powered clocks (Henlein / Germany)•1656, 1675: pendulum clocks, balance wheels (Hyugens, Netherlands)•1920s – : quartz clocks•1949 – : atomic clocks•1967: Cesium clock becomes official standard
Development of modernDevelopment of modern
timekeeping driven by navigationtimekeeping driven by navigation
Before mid-1700sBefore mid-1700sLatitude: use quadrant/sextant/octant to sight
North Star or sunLongitude: lunar time – very poor accuracy
1714:1714: British Parliament sets £20,000 prize ($10M in today’s dollars!) to make clock accurate to 2 minutes (0.5° longitude)
John Harrison – 1764John Harrison – 1764
H4 Linked balance mechanism
Today: GPS and LORAN-CToday: GPS and LORAN-C
We still use clocks to We still use clocks to navigatenavigate
Repetitive MotionsRepetitive Motions• An object with a stable equilibrium
tends to oscillate about that equilibrium• This oscillation involves at least two
types of energy: kinetic and a potential energy
• Once the motion has been started, it will repeat
When energy traded back and forth between When energy traded back and forth between kinetic and potential energy: “resonance”kinetic and potential energy: “resonance”
Mass on springMass on spring
Ball in bowlBall in bowl
Many objects in nature Many objects in nature have natural have natural resonances !resonances !
Repetitive motion characterized by a: period (or frequency) and amplitude
Resonance: energy can be stored in motion at a specific frequency
Period:Period: time of one full cycle
Frequency (1/Period):Frequency (1/Period):cycles completed per second
Amplitude:Amplitude:extent of repetitive motion
In an ideal clock, the period (and In an ideal clock, the period (and frequency) should not depend on frequency) should not depend on amplitudeamplitude
Properties of oscillationProperties of oscillation
Frequency depends on two propertiesFrequency depends on two properties
MassMass(beer gut)
StiffnessStiffness(diving board)
The Harmonic OscillatorThe Harmonic Oscillator
• Anything with a stable equilibrium and a restoring force (F) that’s proportional to the distortion away from equilibrium (x)(F = - k x, where k is a constant)
• Period is independent of amplitude• Examples:
1. Simple pendulum (small amplitude)2. Mass on a spring
A special example of something with a natural resonance
mg
Restoring force
F
PendulumPendulum
A harmonic oscillator!
That indicates simple harmonic motion
At low amplitude, the restoring force is proportional to the distance from equilibrium.
F = - k x (you have already seen this as Hooke’s Law!)
PendulumPendulum
• Period=
• Period only independent of amplitude for small amplitude
2length
g
Near earth’s surface, 1 m Near earth’s surface, 1 m pendulum has a 2 second pendulum has a 2 second periodperiod
Bowling, golf ball pendulaBowling, golf ball pendula
Variable length pendulaVariable length pendula
Chaotic pendulumChaotic pendulum
Clicker Clicker questionquestion
What happens to the period of a swing if you stand up?
A) The period gets longerB) The period gets shorterC) The period doesn’t change!
Balance ring clocksBalance ring clocks
A mass on a spring that is not sensitive to gravityA mass on a spring that is not sensitive to gravity
Balance Ring ClocksBalance Ring Clocks• A torsional coil spring causes a balanced ring to
twist back and forth as a harmonic oscillator• Gravity exerts no torque about the ring’s pivot
Torsion pendulaTorsion pendula
The Main Spring keeps tension on toothed escape wheel and needs to be re-wound.
•Coil Spring attached to Balance Ring and to the body of the watch•Coil Spring provides the restoring force for the Balance Ring•The restoring torque is proportional to the angle of rotation …simple harmonic motion ( = - k )!
Balance Ring ClocksBalance Ring Clocks
Quartz oscillatorsQuartz oscillators
Typical frequency in watch: 32,768 Hz (period is 31 s)
Most modern clocks use a quartz oscillator
Quartz OscillatorsQuartz Oscillators• Crystalline quartz is a harmonic oscillator• Oscillation decay is extremely slow (very pure
tone)• Quartz is piezoelectric
– Mechanically-electrically coupledmotion induced and measured electrically
PiezoelectricityPiezoelectricity
Can think of bonds between atoms in a crystal as springs. So, the restoring force is proportional to the distance from equilibrium. Simple harmonic motion! (F = -k x)
Quartz OscillatorsQuartz Oscillators
Quartz ClocksQuartz Clocks
• Vibration triggers electronic counter• Nearly insensitive to gravity,
temperature,pressure, and acceleration
• Slow vibration decayleads to precise period (loses/gains 0.1 sec in 1 year)
• Different shapes (bars, tuning fork) and cuts
Tuning forkTuning fork
Which clock should Neil Which clock should Neil Armstrong take to the moon?Armstrong take to the moon?
C. Quartz watchB. Balance ring clockA. Grandfather clock
Clicker questionClicker question
Time standardsTime standards
But every Cesium atom is exactly the same!
Courtesy of Mark Raizen’s group
What is one second?What is one second?
Problem: No two pendula or quartz oscillators are exactly the same
Atomic ClocksAtomic Clocks• Particles in an atom (neutrons, protons, electrons) can
have only a very specific amount of total energy.• Changing from one quantum state to another requires
or releases a fixed amount of energy• That energy can be converted into a frequency, so can
be the basis of a very accurate clock.
1 sec = 9,192,631,770 periods of the radiation corresponding to the ground state hyperfine transition in 133Cs
Spectral linesSpectral lines
NIST-F1 Cesium Fountain Atomic ClockThe Primary Time and Frequency
Standard for the United States
Atomic ClocksAtomic Clocks
Loses less than one second in 60 million years
NIST-7NIST-F1
F1 – the fountain clockF1 – the fountain clock
Every GPS satelliteEvery GPS satellite
contains an atomic clockcontains an atomic clock
Receivers: high quality quartz clock which is synchronized to atomic clock
See you next class!
For next class: Read Section 9.2
Bring a musical instrument!