Oscillations: clocks and music

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Oscillations clocks and music
Masses and springs again Pendula and
grandfathers clocks John Harrison and the map
of the world
Chicago Does anybody really know what time it is?
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History

• B.C.E. 742 Sun dials
• A.D. 885 Striped candles as clocks
• A.D. 1657 Huygens pendulum clocks
• A.D. 1704 Jeweled bearings for low friction
• A.D. 1735 Small portable clocks for ships
• A.D. 1840 First electric clocks
• A.D. 1918 AC synchronous electric motor clocks
• A.D. 1921 Quartz oscillator clocks
• A.D. 1955 Atomic clocks

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One of the great inventions

• Hour-glasses, Water clocks, Candles are
  non-repeating, and so not so useful.

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The ultimate time keeper

• Oscillations of mass on a spring repeat cycle
  after cycle
• after cycle.

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x
t
x
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Pendulum oscillator

• For small oscillations
• restoring force is proportional to
• displacement (just like the spring)
• So the same kind
• of oscillations
• occur

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Constant period of oscillation

• Spring F - kx leads to period that depend on
  mass but not amplitude

Pendulum F - mg sin? and period depends on
length but not mass
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Harmonic (or linear) oscillation

• Period of oscillation, or its inverse the
• Frequency, does not depend on the
• Amplitude of oscillation
• In any oscillator in the real world there are
  imperfections
• friction that damps the oscillation amplitude
• non-linearity that makes the period vary with
  amplitude
• Engineers have managed 1 part per billion damping
• and clever amplitude controls to maintain
  accuracy

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Why are grandfather clocks all the same size?

• Clock mechanism is driven by descent of a weight
  and the descent is timed by the pendulum period
  through a pawl or escapement.
• Clocks ticks once per second so
• pendulum period is two seconds
• L (Dt)2g / 4p2 (4)(10)/(4)(10)
• 1m

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Now move the clock hands

• Pawl clicks each second for each half
• cycle of the pendulum

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But this doesnt work in an pitching boat

• Remember how Thandie Newton weighed too much in
  the
• accelerating elevator?
• Vessel motion changes pendulum motion
• weather changes period as parts expand or shrink
  
• (plus the dang things were just too heavy)
• Enter John Harrison who redesigned the mechanisms
  and built more compact, reliable, and portable
  clocks.
• http//www.nmm.ac.uk/server/show/conWebDoc.355/vie
  wPage/1

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Unsung hero of engineering

• Harrison
• Use opposing oscillations and a new pendulum
  design on ships for accurate time-keeping and
  hence accurate navigation
• Everyone else Mo money!
• Harrisons cut was 20,000
• (about 3,000,000 today)

Harrisons H1 1735
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Harrisons grandchild

• Rolex mainspring drives
• the balanced ring as a
• harmonic oscillator
• Gravity creates no net torque
• on the balanced ring
• Pawls create only irrelevant disturbances in the
  oscillation period.

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The real watch is a little more complicated
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Tuning fork oscillator

• Musicians use tailored spring oscillators as
  reference tones
• because the frequency does not change much
  (mostly because it very high)
• Arms of the fork are both m and k, and damping is
  very low

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More than just a lightening rod

• Armonica, aka
• glass harmonica,
• used spring oscillators,
• (rims of wine glasses)
• to play music

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Quartz tuning forks

• Sand commerce quartz is just snobbish dirt (SiO2
  crystal)
• Piezoelectric response under strain it makes an
  electrical signal
• Oscillation frequency (32,000 Hz)
• and amplitude can be
• measured and driven electrically
• with excellent efficiency

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Silicon Sub-micro Oscillators

• Very high oscillation frequency (100,000,000 Hz)
  because mass is so small
• Change in frequency can be used to weigh viruses
  and big molecules

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The Atomic Clock NIST Cs fountain standard
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Quantum clock

• Energy difference between electron states
• is very well controlled if atoms are
• not bumping into each other too often
• Energy hPlanck ? frequency
• So electron bouncing between energy levels
  (orbits around the nucleus) makes a clock that
  is very accurate at frequency of 9,000,000,000 Hz
• Frequency is accurate/stable to about 1 part per
  billion

DE
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Take home messages

• Time keeping is easy to think about
• but tough to do accurately
• Springs and masses are harmonic oscillators
• period
• A pendulum is a harmonic oscillator for small
  amplitudes and
• do not depend on pendulum mass