9.1 Clocks

1. 9.1 Clocks New ideas for today • Resonance • Harmonic oscillators • Timekeeping

2. History of timekeeping Earliest clocks: Egypt • ~3500 BC: sundials • ~1500 BC: water clocks 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

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

4. 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 Linked balance mechanism H4

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

6. Ball in bowl Repetitive Motions Mass on spring • 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”

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

8. Properties of oscillation Period:time of one full cycle Frequency (1/Period):cycles completed per second Amplitude:extent of repetitive motion In an ideal clock, the period (and frequency) should not depend on amplitude

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

10. The Harmonic Oscillator A special example of something with a natural resonance • Anything with a stable equilibrium and a restoring force (F) that’s proportional to the distortion away from equilibrium (x) (F = -kx, where k is a constant) • Period is independent of amplitude • Examples: 1. Simple pendulum (small amplitude) 2. Mass on a spring

11. Pendulum A harmonic oscillator! F Restoring force mg

12. 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!) That indicates simple harmonic motion

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

14. 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!

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

16. Torsion pendula 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

18. Balance Ring Clocks • 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 (t = - k q)! TheMain Spring keeps tension on toothed escape wheel and needs to be re-wound.

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

21. Piezoelectricity 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

22. Quartz Oscillators 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)

23. Tuning fork Quartz 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

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

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

26. Spectral lines 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 133Cs

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

28. NIST-F1 NIST-7

29. F1 – the fountain clock

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

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