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9.1 Clocks New ideas for today Resonance Harmonic oscillators Timekeeping

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~3500 BC: sundials ~1500 BC: water clocks History of timekeeping Earliest clocks: Egypt Modern 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

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Development of modern timekeeping driven by navigation timekeeping driven by navigation Before mid-1700s Latitude: use quadrant/sextant/octant to sight North Star or sun Longitude: lunar time – very poor accuracy

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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 – 1764 H4 Linked balance mechanism

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Today: GPS and LORAN-C We still use clocks to navigate

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Repetitive 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 kinetic and potential energy: “resonance” Mass on spring Ball in bowl

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Many objects in nature have natural resonances ! Repetitive motion characterized by a: period (or frequency) and amplitude Resonance: energy can be stored in motion at a specific frequency

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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 frequency) should not depend on amplitude Properties of oscillation

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Frequency depends on two properties Mass Mass (beer gut) Stiffness Stiffness (diving board)

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The 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

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mg Restoring force F Pendulum A harmonic oscillator!

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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!)

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Pendulum Period= Period only independent of amplitude for small amplitude Near earth’s surface, 1 m pendulum has a 2 second period Bowling, golf ball pendula Variable length pendula Chaotic pendulum

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Clicker question What happens to the period of a swing if you stand up? A) The period gets longer B) The period gets shorter C) The period doesn’t change!

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Balance ring clocks A mass on a spring that is not sensitive to gravity

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Balance 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 pendula

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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 Clocks

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Quartz oscillators Typical frequency in watch: 32,768 Hz (period is 31 s) Most modern clocks use a quartz oscillator

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Quartz Oscillators Crystalline quartz is a harmonic oscillator Oscillation decay is extremely slow (very pure tone) Quartz is piezoelectric –Mechanically-electrically coupled motion induced and measured electrically Piezoelectricity

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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 Oscillators

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Quartz Clocks Vibration triggers electronic counter Nearly insensitive to gravity, temperature, pressure, and acceleration Slow vibration decay leads to precise period (loses/gains 0.1 sec in 1 year) Different shapes (bars, tuning fork) and cuts Tuning fork

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Which clock should Neil Armstrong take to the moon? C. Quartz watch B. Balance ring clockA. Grandfather clock Clicker question

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Time standards But every Cesium atom is exactly the same! Courtesy of Mark Raizen’s group What is one second? Problem: No two pendula or quartz oscillators are exactly the same

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Atomic 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 133 Cs Spectral lines

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NIST-F1 Cesium Fountain Atomic Clock The Primary Time and Frequency Standard for the United States Atomic Clocks Loses less than one second in 60 million years

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NIST-7 NIST-F1

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F1 – the fountain clock

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Every GPS satellite contains an atomic clock Receivers: high quality quartz clock which is synchronized to atomic clock

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See you next class! For next class: Read Section 9.2 Bring a musical instrument!

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