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Oscillations in the spring-mass system

Oscillations in the spring-mass system. Maximum speed, maximum kinetic energy. Maximum force, maximum acceleration. Will the period change if the amplitude changes?. period. Frequency and period are not dependend on the amplitude! What are the implications for musical instruments?

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Oscillations in the spring-mass system

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  1. Oscillations in the spring-mass system Maximum speed, maximum kinetic energy Maximum force, maximum acceleration

  2. Will the period change if the amplitude changes? period

  3. Frequency and period are not dependend on the amplitude! • What are the implications for musical instruments? • Pitch is not dependent on how much the string is plucked (for example)

  4. Does the period depend on the mass? Which force is acting on both masses? Which acceleration does each mass experience? The smaller mass accelerates at a higher rate: it is faster to move through the cycle. It will oscillate at a smaller period (faster).

  5. Properties of the spring and period Large k means high acceleration High acceleration means a cycle is completed fast soft stiff Small spring constant k2 Large spring constant k1 High k <-> low period

  6. Factors influencing the period:

  7. Frequency and Period

  8. Simple harmonic motion What is influenced by the amplitude?

  9. What happens if energy gets lost due to friction? • A) the frequency decreases • B) the period decreases • C) the amplitude decreases • D) all of the above

  10. The amplitude decreases. Frequency and period stay the same. Damped harmonic motion

  11. Example Clink of a coffee cup

  12. Example • Finger flicking Short, hard to assign pitch

  13. Driven oscillator f0 < f Slow driving frequency: Mass moves in rhythm with the driver.

  14. f0 > f Driven oscillator Fast driving frequency: The mass is practically not moving.

  15. f0 = f Driven oscillator Resonance: Amplitude grows very much!

  16. Amplitude versus driving frequency Resulting amplitude Natural frequency of oscillator Driving frequency

  17. The shocks of an automobile are springs. Which of the following would be desirable? • A) resonance with the bumps on the road, and little damping • B) high damping and high spring constant • C) high damping and very low spring constant • D) resonance with the bumps on the road, and high damping

  18. A) resonance with the bumps on the road, and little damping

  19. B) high damping and high spring constant One bump, high spring constant, medium damping One bump, high damping, medium spring constant Several bumps, high damping, medium spring constant Answer C: similar effects

  20. D) resonance with the bumps on the road, and high damping Multiple bumps

  21. Examples of other oscillators • Pendulum (small amplitude) L

  22. Examples of other oscillators • Air-filled piston Atmospheric Pressure P0 Atmospheric Pressure P0 Atmospheric Pressure P0 F=pA m m m A P0 P0+p P0-p L air air air

  23. Examples of other oscillators • Helmholtz Resonator A L V

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