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What are These? Jerry Gilfoyle Biological Attack! 1 / 23 What are These? Anthrax spores Jerry Gilfoyle Biological Attack! 1 / 23 Until the 20th century, anthrax killed hundreds 1 What are These? of thousands of people and animals each

  1. What are These? Jerry Gilfoyle Biological Attack! 1 / 23

  2. What are These? Anthrax spores Jerry Gilfoyle Biological Attack! 1 / 23

  3. Until the 20th century, anthrax killed hundreds 1 What are These? of thousands of people and animals each year. Anthrax spores Jerry Gilfoyle Biological Attack! 1 / 23

  4. Until the 20th century, anthrax killed hundreds 1 What are These? of thousands of people and animals each year. Even now for an inhaled anthrax infection the 2 risk of death is 50-80% despite treatment. Anthrax spores Jerry Gilfoyle Biological Attack! 1 / 23

  5. Until the 20th century, anthrax killed hundreds 1 What are These? of thousands of people and animals each year. Even now for an inhaled anthrax infection the 2 risk of death is 50-80% despite treatment. A long-standing fear is a biological attack using 3 an agent like anthrax or smallpox. The natural spread of the disease and its indis- 4 criminate nature can amplify the impact. Anthrax spores Jerry Gilfoyle Biological Attack! 1 / 23

  6. Until the 20th century, anthrax killed hundreds 1 What are These? of thousands of people and animals each year. Even now for an inhaled anthrax infection the 2 risk of death is 50-80% despite treatment. A long-standing fear is a biological attack using 3 an agent like anthrax or smallpox. The natural spread of the disease and its indis- 4 criminate nature can amplify the impact. Anthrax spores Some weaponized forms could cause mass ca- 5 sualties. Defense against such an attack is focused on 6 rapid identification and mitigation. Jerry Gilfoyle Biological Attack! 1 / 23

  7. Have We Been Attacked? 1 The attack will not be obvious; it may take hours or days to know. 2 Current biological diagnostics are very effective, but they’re slow. 3 Fast response time is essential to avoid overwhelming the health-care system ⇒ rapid response is vital . Jerry Gilfoyle Biological Attack! 2 / 23

  8. Have We Been Attacked? 1 The attack will not be obvious; it may take hours or days to know. 2 Current biological diagnostics are very effective, but they’re slow. 3 Fast response time is essential to avoid overwhelming the health-care system ⇒ rapid response is vital . 4 Nanosized oscillators - cantilevers can be coated with antibodies to bind to spores of specific diseases. 5 As the spores bind, the oscillations of the device change. 6 The change is measured by deflection of a laser beam shining on the cantilever. Jerry Gilfoyle Biological Attack! 2 / 23

  9. A Nanosized Biosensor You’re a program manager for DARPA and you’re evaluating a proposal to use a nano-sized cantilever to detect the presence of anthrax spores. To test the validity of the proposal consider the following problem. The cantilever can be treated as a simple harmonic oscillator of mass m c (see below). Suppose n a = 300 anthrax spores each with mass m a = 10 − 15 kg accumulate on the cantilever beam. What is the change ∆ ω in the angular frequency of the cantilever? We can detect angular frequency changes of ≈ 10 6 rad / s . Is this change detectable? WILL IT WORK? L c = 100 µ m y m c = 1 . 49 × 10 − 12 kg 0 k 0 = 370 kg / s 2 Jerry Gilfoyle Biological Attack! 3 / 23

  10. The Harmonic Oscillator 1 The Force: F s = − kx where x is the displacement from equilibrium. Jerry Gilfoyle Biological Attack! 4 / 23

  11. The Harmonic Oscillator 1 The Force: F s = − kx where x is the displacement from equilibrium. 2 Measurements: ∆ t=− φ/ω v (m/s) y (m) Time (s) Jerry Gilfoyle Biological Attack! 4 / 23

  12. The Harmonic Oscillator 1 The Force: F s = − kx where x is the displacement from equilibrium. 2 Measurements: ∆ t=− φ/ω v (m/s) y (m) Time (s) 3 The Solution: x ( t ) = A cos ( ω t + φ ) Jerry Gilfoyle Biological Attack! 4 / 23

  13. The Harmonic Oscillator 1 The Force: F s = − kx where x is the displacement from equilibrium. 2 Measurements: ∆ t=− φ/ω v (m/s) y (m) Time (s) 3 The Solution: x ( t ) = A cos ( ω t + φ ) 4 Newton’s Second Law yields d 2 x ( t ) = − k mx ( t ) dt 2 Parameters: � k T = 2 π f = 1 ω = A and φ are initial con- m ω T ditions. Jerry Gilfoyle Biological Attack! 4 / 23

  14. The Derivative of the Sine 1.5 1 0.5 f(x) 0 sin(x) dsin(x)/dx -0.5 -1 -1.5 0 1 2 3 4 5 6 7 8 9 10 x Jerry Gilfoyle Biological Attack! 5 / 23

  15. The Derivative of the Sine 1.5 1 0.5 f(x) 0 sin(x) dsin(x)/dx -0.5 -1 -1.5 0 1 2 3 4 5 6 7 8 9 10 x Jerry Gilfoyle Biological Attack! 6 / 23

  16. The Derivative of the Sine 1.5 1 0.5 sin(x) f(x) 0 dsin(x)/dx -0.5 cos(x) -1 -1.5 0 1 2 3 4 5 6 7 8 9 10 x Jerry Gilfoyle Biological Attack! 7 / 23

  17. The Derivative of the Sine 1.5 1 0.5 sin(x) f(x) 0 dsin(x)/dx cos(x) -0.5 dcos(x)/dx -1 -1.5 0 1 2 3 4 5 6 7 8 9 10 x Jerry Gilfoyle Biological Attack! 8 / 23

  18. The Harmonic Oscillator 1 The Force: F s = − kx where x is the displacement from equilibrium. 2 Measurements: ∆ t=− φ/ω v (m/s) y (m) Time (s) 3 The Solution: x ( t ) = A cos ( ω t + φ ) 4 Newton’s Second Law yields d 2 x ( t ) = − k mx ( t ) dt 2 Jerry Gilfoyle Biological Attack! 9 / 23

  19. The Harmonic Oscillator 1 The Force: F s = − kx where x is the displacement from equilibrium. 2 Measurements: ∆ t=− φ/ω v (m/s) y (m) Time (s) 3 The Solution: x ( t ) = A cos ( ω t + φ ) 4 Newton’s Second Law yields d 2 x ( t ) = − k mx ( t ) dt 2 5 Parameters: � T = 2 π f = 1 k ω = A and φ are initial con- ω m T ditions. Jerry Gilfoyle Biological Attack! 9 / 23

  20. Music! The end of the prong of a tuning fork that executes simple harmonic motion with a frequency of 1024 Hz has an amplitude A = 0 . 4 mm . What is the maximum velocity v max and maximum acceleration a max of the end of a prong? What is the angular frequency? What is the speed of the end of the prong when the displacement from equilibrium is x 1 = 0 . 1 mm ? Jerry Gilfoyle Biological Attack! 10 / 23

  21. Energy in the Harmonic Oscillator Carbon and oxygen are bound together by a force that can be modeled as a harmonic oscillator (see below). If the angular frequency is ω = 3 . 8 × 10 14 rad / s and the mass is m = 1 . 14 × 10 − 26 kg , then what is the spring constant k ? If the energy of the ground state is E = 2 × 10 − 20 J , then what is the amplitude of the oscillation? Jerry Gilfoyle Biological Attack! 11 / 23

  22. How Do you Weigh a Weightless Person? To weigh astronauts on the International Space Station NASA uses a chair of mass m c mounted on a spring of spring constant k c = 605 . 6 N / m that is anchored to the spacecraft. The period of the oscillation of the empty chair is T c = 0 . 90149 s . When an astronaut is sitting in the chair the new period is T a = 2 . 12151 s . What is the mass of the astronaut? Jerry Gilfoyle Biological Attack! 12 / 23

  23. Medical Oscillators? A transducer used in medical ultrasound imaging is a very thin disk ( m = 0 . 10 g ) oscillating back and forth at a frequency f = 10 6 Hz driven by an electromagnetic coil. The maximum restoring force that can be applied to the disk without breaking it is F max = 40 , 000 N . (a) What is the maximum oscillation amplitude that won’t rupture the disk? (b) What is the disk’s maximum speed at this amplitude? Jerry Gilfoyle Biological Attack! 13 / 23

  24. A Nanosized Biosensor You’re a program manager for DARPA and you’re evaluating a proposal to use a nano-sized cantilever to detect the presence of anthrax spores. To test the validity of the proposal consider the following problem. The cantilever can be treated as a simple harmonic oscillator of mass m c (see below). Suppose n a = 300 anthrax spores each with mass m a = 10 − 15 kg accumulate on the cantilever beam. What is the change ∆ ω in the angular frequency of the cantilever? We can detect angular frequency changes of ≈ 10 6 rad / s . Is this change detectable? WILL IT WORK? DO YOU GIVE THEM TAXPAYER DOLLARS? L c = 100 µ m y m c = 1 . 49 × 10 − 12 kg 0 k 0 = 370 kg / s 2 Jerry Gilfoyle Biological Attack! 14 / 23

  25. An Oscillating Cantilever Jerry Gilfoyle Biological Attack! 15 / 23

  26. Hints for Periodic Motion 1 Use the factory defaults for the force transducer calibration. Click Calibration (left side of Capstone GUI). 1 Click Force . 2 Click Next . 3 Click Restore Factory Settings . 4 Click Calibration . 5 2 Set the Sampling Rate to 50-100 Hz (Bottom of Capstone GUI). 3 Tare before every measurement (side of Force transducer). 4 Be gentle. Jerry Gilfoyle Biological Attack! 16 / 23

  27. The Harmonic Oscillator Approximation Periodic Motion 2.0 〈 ME 〉 = 0.025 J Δ ME = 0.003 J 1.5 Counts 1.0 0.5 0.0 0.015 0.020 0.025 0.030 0.035 ME ( J ) Jerry Gilfoyle Biological Attack! 17 / 23

  28. The Center of Mass Frame of Reference Jerry Gilfoyle Biological Attack! 18 / 23

  29. Harmonic Oscillator Waveform Phase Shift Period Amplitude Position Time Jerry Gilfoyle Biological Attack! 19 / 23

  30. The Harmonic Oscillator 1 The Force: F s = − kx where x is the displacement from equilibrium. 2 The Potential Energy: V s ( x ) = 1 2 kx 2 3 Measurements: y (m) ∆ t=− φ/ω v (m/s) a (m/s ) 2 Force (N) Time (s) 4 The Solution: x ( t ) = A cos ( ω t + φ ) 5 Parameters: � T = 2 π f = 1 k A and φ are initial con- ω = ω m T ditions. Jerry Gilfoyle Biological Attack! 20 / 23

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