1. Clocks 1 Clocks

2. Clocks 2 Introductory Question You’re bouncing gently up and down at the end of a springboard, without leaving the board’s surface. If you bounce harder, the time it takes for each bounce will You’re bouncing gently up and down at the end of a springboard, without leaving the board’s surface. If you bounce harder, the time it takes for each bounce will A. become shorter B. become longer C. remain the same

3. Clocks 3 Observations About Clocks They divide time into uniform intervals They divide time into uniform intervals They count the passage of those intervals They count the passage of those intervals Some involve obvious mechanical motions Some involve obvious mechanical motions Some seem to involve no motion at all Some seem to involve no motion at all They require an energy source They require an energy source They have limited accuracy They have limited accuracy

4. Clocks 4 4 Questions about Clocks Why don’t we use hourglasses any more? Why don’t we use hourglasses any more? Are all repetitive motions equally accurate? Are all repetitive motions equally accurate? Why are some watches more accurate? Why are some watches more accurate? How do clocks use harmonic oscillators? How do clocks use harmonic oscillators?

5. Clocks 5 Question 1 Why don’t we use hourglasses any more? Why don’t we use hourglasses any more?

6. Clocks 6 Non-Repetitive Clocks Devices that measure a single interval of time Devices that measure a single interval of time Sandglasses Sandglasses Water clocks Water clocks Candles Candles Though common in antiquity, Though common in antiquity, they are poorly suited to subdividing the day they are poorly suited to subdividing the day They require frequent operator intervention They require frequent operator intervention and that operator requirement limits accuracy and that operator requirement limits accuracy

7. Clocks 7 Repetitive Motions Repetitive motions measure many intervals Repetitive motions measure many intervals A device with a stable equilibrium A device with a stable equilibrium tends to oscillate about that equilibrium tends to oscillate about that equilibrium and its oscillation entails at least two types of energy and its oscillation entails at least two types of energy kinetic energy kinetic energy a potential energy (e.g., gravitational, elastic, magnetic) a potential energy (e.g., gravitational, elastic, magnetic) Once started, this motion repeats spontaneously Once started, this motion repeats spontaneously

8. Clocks 8 Repetitive-Motion Clocks Developed about 500 years ago Developed about 500 years ago Require no operator intervention Require no operator intervention Accuracy limited only by the repetitive motion Accuracy limited only by the repetitive motion Motion shouldn’t depend on externals such as Motion shouldn’t depend on externals such 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 motion or the mechanism that observes the motion

9. Clocks 9 Question 2 Are all repetitive motions equally accurate? Are all repetitive motions equally accurate?

10. Clocks 10 Some Specifics A little terminology A little terminology Period: time of full repetitive motion cycle Period: time of full repetitive motion cycle Frequency: cycles completed per unit of time Frequency: cycles completed per unit of time Amplitude: peak extent of repetitive motion Amplitude: peak extent of repetitive motion An important application of that terminology An important application of that terminology In an ideal clock, the repetitive motion’s period shouldn’t depend on its amplitude In an ideal clock, the repetitive motion’s period shouldn’t depend on its amplitude

11. Clocks 11 Harmonic Oscillators (Part 1) A harmonic oscillator A harmonic oscillator has a stable equilibrium and a restoring force that’s proportional to displacement from that equilibrium has a stable equilibrium and a restoring force that’s proportional to displacement from that equilibrium has a period that’s independent of amplitude has a period that’s independent of amplitude At its heart, a harmonic oscillator consists of At its heart, a harmonic oscillator consists of an inertial object – a mass an inertial object – a mass and a springlike restoring force – a spring and a springlike restoring force – a spring

12. Clocks 12 Harmonic Oscillators (Part 2) The period of a harmonic oscillator decreases as The period of a harmonic oscillator decreases as the mass becomes smaller – less inertia the mass becomes smaller – less inertia the spring becomes stiffer – a stiffer restoring force the spring becomes stiffer – a stiffer restoring force Common harmonic oscillators include Common harmonic oscillators include a mass on a spring (the prototypical form) a mass on a spring (the prototypical form) a pendulum a pendulum a flagpole a flagpole a tuning fork a tuning fork

13. Clocks 13 Introductory Question (revisited) You’re bouncing gently up and down at the end of a springboard, without leaving the board’s surface. If you bounce harder, the time it takes for each bounce will You’re bouncing gently up and down at the end of a springboard, without leaving the board’s surface. If you bounce harder, the time it takes for each bounce will A. become shorter B. become longer C. remain the same

14. Clocks 14 Question 3 Why are some watches more accurate? Why are some watches more accurate?

15. Clocks 15 The Limits to the Accuracy Clocks exhibit fundamental limits: Clocks exhibit fundamental limits: Oscillation decay limits preciseness of period Oscillation decay limits preciseness of period Clocks also exhibit practical limits: Clocks also exhibit practical limits: Sustaining motion can influence the period Sustaining motion can influence the period Observing the period can influence the period Observing the period can influence the period Sensitivity to temperature, pressure, wind, … Sensitivity to temperature, pressure, wind, …

16. Clocks 16 Question 4 How do clocks use harmonic oscillators? How do clocks use harmonic oscillators?

17. Clocks 17 Pendulums Pendulum (almost) a harmonic oscillator Pendulum (almost) a harmonic oscillator Period proportional to (length/gravity) 1/2 Period proportional to (length/gravity) 1/2 Period (almost) independent of amplitude Period (almost) independent of amplitude

18. Clocks 18 Pendulum Clocks Pendulum is clock’s timekeeper Pendulum is clock’s timekeeper For accuracy, the pendulum For accuracy, the pendulum pivot–center-of-gravity distance is pivot–center-of-gravity distance is temperature stabilized temperature stabilized adjustable for local gravity effects adjustable for local gravity effects streamlined to minimize air drag streamlined to minimize air drag motion sustained, measured gently motion sustained, measured gently Limitation: clock mustn't move Limitation: clock mustn't move

19. Clocks 19 Balance Ring Clocks A torsional spring causes a balance-ring harmonic oscillator to twist back and forth A torsional spring causes a balance-ring harmonic oscillator to twist back and forth Gravity exerts no torque about the ring’s pivot and has no influence on the period Gravity exerts no torque about the ring’s pivot and has no influence on the period Twisting is sustained and measured with minimal effects on the ring’s motion Twisting is sustained and measured with minimal effects on the ring’s motion

20. Clocks 20 Quartz Oscillators Crystalline quartz is a harmonic oscillator Crystalline quartz is a harmonic oscillator Crystal provides the inertial mass Crystal provides the inertial mass Stiffness provides restoring force Stiffness provides restoring force Oscillation decay is extremely slow Oscillation decay is extremely slow Fundamental accuracy is very high Fundamental accuracy is very high Quartz is piezoelectric Quartz is piezoelectric mechanical and electrical changes coupled mechanical and electrical changes coupled motion is induced and measured electrically motion is induced and measured electrically

21. Clocks 21 Quartz Clocks Electronic system starts crystal vibrating Electronic system starts crystal vibrating Vibrating crystal triggers electronic counter Vibrating crystal triggers electronic counter Nearly insensitive to gravity, temperature, pressure, and acceleration Nearly insensitive to gravity, temperature, pressure, and acceleration Slow vibration decay leads to precise period Slow vibration decay leads to precise period Tuning-fork shape yields slow, efficient vibration Tuning-fork shape yields slow, efficient vibration

22. Clocks 22 Summary about Clocks Most clocks involve harmonic oscillators Most clocks involve harmonic oscillators Amplitude independence aids accuracy Amplitude independence aids accuracy Clock sustains and counts oscillations Clock sustains and counts oscillations Oscillators that lose little energy work best Oscillators that lose little energy work best