Clocks 1

ClocksClocks

Clocks 2

Introductory QuestionIntroductory Question

You’re bouncing gently up and down You’re bouncing gently up and down at the end of a springboard, without at the end of a springboard, without leaving the board’s surface. If you leaving the board’s surface. If you bounce harder, the time it takes for bounce harder, the time it takes for each bounce willeach bounce will

A.A. become shorterbecome shorter

B.B. become longerbecome longer

C.C. remain the sameremain the same

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Observations About Observations About ClocksClocks

They divide time into uniform intervalsThey divide time into uniform intervals They count the passage of those They count the passage of those

intervalsintervals Some involve obvious mechanical Some involve obvious mechanical

motionsmotions Some seem to involve no motion at allSome seem to involve no motion at all They require an energy sourceThey require an energy source They have limited accuracyThey have limited accuracy

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4 Questions about Clocks4 Questions about Clocks

Why don’t we use hourglasses any Why don’t we use hourglasses any more?more?

Are all repetitive motions equally Are all repetitive motions equally accurate?accurate?

Why are some watches more Why are some watches more accurate?accurate?

How do clocks use harmonic How do clocks use harmonic oscillators?oscillators?

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Question 1Question 1

Why don’t we use hourglasses any Why don’t we use hourglasses any more?more?

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Non-Repetitive ClocksNon-Repetitive Clocks

Devices that measure a single interval of Devices that measure a single interval of timetime SandglassesSandglasses Water clocksWater clocks CandlesCandles

Though common in antiquity,Though common in antiquity, they are poorly suited to subdividing the they are poorly suited to subdividing the

dayday They require frequent operator interventionThey require frequent operator intervention and that operator requirement limits accuracyand that operator requirement limits accuracy

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Repetitive MotionsRepetitive Motions

Repetitive motions measure many Repetitive motions measure many intervalsintervals

A device with a stable equilibriumA device with a stable equilibrium tends to oscillate about that equilibriumtends to oscillate about that equilibrium and its oscillation entails at least two types of and its oscillation entails at least two types of

energyenergy kinetic energykinetic energy a potential energy (e.g., gravitational, elastic, a potential energy (e.g., gravitational, elastic,

magnetic)magnetic) Once started, this motion repeats Once started, this motion repeats

spontaneouslyspontaneously

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Repetitive-Motion ClocksRepetitive-Motion Clocks

Developed about 500 years agoDeveloped about 500 years ago Require no operator interventionRequire no operator intervention Accuracy limited only by the repetitive Accuracy limited only by the repetitive

motionmotion Motion shouldn’t depend on externals Motion shouldn’t depend on externals

such assuch as the temperature, air pressure, or time of day,the temperature, air pressure, or time of day, the clock’s store of energy,the clock’s store of energy, or the mechanism that observes the motionor the mechanism that observes the motion

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Question 2Question 2

Are all repetitive motions equally Are all repetitive motions equally accurate?accurate?

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Some SpecificsSome Specifics

A little terminologyA little terminology Period: time of full repetitive motion cycle Period: time of full repetitive motion cycle Frequency: cycles completed per unit of timeFrequency: cycles completed per unit of time Amplitude: peak extent of repetitive motionAmplitude: peak extent of repetitive motion

An important application of that An important application of that terminologyterminology In an ideal clock, the repetitive motion’s In an ideal clock, the repetitive motion’s

period shouldn’t depend on its amplitudeperiod shouldn’t depend on its amplitude

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Harmonic Oscillators Harmonic Oscillators (Part (Part 1)1)

A harmonic oscillatorA harmonic oscillator has a stable equilibrium and a restoring has a stable equilibrium and a restoring

force that’s proportional to displacement force that’s proportional to displacement from that equilibriumfrom that equilibrium

has a period that’s independent of has a period that’s independent of amplitudeamplitude

At its heart, a harmonic oscillator At its heart, a harmonic oscillator consists ofconsists of an inertial object – a massan inertial object – a mass and a springlike restoring force – a springand a springlike restoring force – a spring

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Harmonic Oscillators Harmonic Oscillators (Part (Part 2)2)

The period of a harmonic oscillator The period of a harmonic oscillator decreases asdecreases as the mass becomes smaller – less inertiathe mass becomes smaller – less inertia the spring becomes stiffer – a stiffer restoring the spring becomes stiffer – a stiffer restoring

forceforce Common harmonic oscillators includeCommon harmonic oscillators include

a mass on a spring (the prototypical form)a mass on a spring (the prototypical form) a penduluma pendulum a flagpolea flagpole a tuning forka tuning fork

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Introductory Question Introductory Question (revisited)(revisited)

You’re bouncing gently up and down You’re bouncing gently up and down at the end of a springboard, without at the end of a springboard, without leaving the board’s surface. If you leaving the board’s surface. If you bounce harder, the time it takes for bounce harder, the time it takes for each bounce willeach bounce will

A.A. become shorterbecome shorter

B.B. become longerbecome longer

C.C. remain the sameremain the same

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Question 3Question 3

Why are some watches more Why are some watches more accurate?accurate?

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The Limits to the The Limits to the AccuracyAccuracy

Clocks exhibit fundamental limits:Clocks exhibit fundamental limits: Oscillation decay limits preciseness of Oscillation decay limits preciseness of

periodperiod Clocks also exhibit practical limits:Clocks also exhibit practical limits:

Sustaining motion can influence the periodSustaining motion can influence the period Observing the period can influence the Observing the period can influence the

periodperiod Sensitivity to temperature, pressure, wind, Sensitivity to temperature, pressure, wind,

……

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Question 4Question 4

How do clocks use harmonic How do clocks use harmonic oscillators?oscillators?

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Pendulums Pendulums

Pendulum (almost) a harmonic Pendulum (almost) a harmonic oscillatoroscillator

Period proportional to Period proportional to (length/gravity)(length/gravity)1/21/2

Period (almost) independent of Period (almost) independent of amplitudeamplitude

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Pendulum ClocksPendulum Clocks

Pendulum is clock’s timekeeperPendulum is clock’s timekeeper For accuracy, the pendulumFor accuracy, the pendulum

pivot–center-of-gravity distance ispivot–center-of-gravity distance is temperature stabilizedtemperature stabilized adjustable for local gravity effectsadjustable for local gravity effects

streamlined to minimize air dragstreamlined to minimize air drag motion sustained, measured gentlymotion sustained, measured gently

Limitation: clock mustn't moveLimitation: clock mustn't move

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Balance Ring ClocksBalance Ring Clocks

A torsional spring causes a balance-A torsional spring causes a balance-ring harmonic oscillator to twist ring harmonic oscillator to twist back and forthback and forth

Gravity exerts no torque about the Gravity exerts no torque about the ring’s pivot and has no influence on ring’s pivot and has no influence on the periodthe period

Twisting is sustained andTwisting is sustained andmeasured with minimalmeasured with minimaleffects on the ring’s motioneffects on the ring’s motion

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Quartz OscillatorsQuartz Oscillators

Crystalline quartz is a harmonic Crystalline quartz is a harmonic oscillatoroscillator Crystal provides the inertial massCrystal provides the inertial mass Stiffness provides restoring forceStiffness provides restoring force

Oscillation decay is extremely slowOscillation decay is extremely slow Fundamental accuracy is very highFundamental accuracy is very high Quartz is piezoelectricQuartz is piezoelectric

mechanical and electrical changes coupledmechanical and electrical changes coupled motion is induced and measured electricallymotion is induced and measured electrically

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Quartz ClocksQuartz Clocks

Electronic system starts crystal vibratingElectronic system starts crystal vibrating Vibrating crystal triggers electronic Vibrating crystal triggers electronic

countercounter Nearly insensitive to gravity, temperature,Nearly insensitive to gravity, temperature,

pressure, and accelerationpressure, and acceleration Slow vibration decaySlow vibration decay

leads to precise periodleads to precise period Tuning-fork shape yieldsTuning-fork shape yields

slow, efficient vibrationslow, efficient vibration

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Summary about ClocksSummary about Clocks

Most clocks involve harmonic Most clocks involve harmonic oscillatorsoscillators

Amplitude independence aids Amplitude independence aids accuracyaccuracy

Clock sustains and counts Clock sustains and counts oscillationsoscillations

Oscillators that lose little energy Oscillators that lose little energy work bestwork best