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Lab 6: Forced Harmonic Motion

This lab explores forced harmonic motion and driven harmonic oscillation. It covers topics such as amplitude of displacement and velocity, resonance, phase changes, energy flow, power, and quality factor. Learn how to measure phase using the Lock-in method.

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Lab 6: Forced Harmonic Motion

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  1. Lab 6: Forced Harmonic Motion • Driven harmonic oscillation Example: Atomic force microscope watch, circuit, …

  2. A constant energy flow at steady state

  3. Forced harmonic oscillation (steady state)

  4. Forced harmonic oscillation (cont.)

  5. Forced harmonic oscillation (cont.)

  6. Forced harmonic oscillation (cont.) Amplitude of displacement: Amplitude of velocity:

  7. Amplitude peaks at 0 resonance

  8. vmax peaks at 0 resonance

  9. Phase changes sharply at resonance

  10. Forced harmonic oscillation (log scale)

  11. Energy that flows in (drive) The power P supplied by F is: The average over one cycle is power factor

  12. Energy that flows out (dissipation) The power P dissipated by Fd is: The average over one cycle is

  13. Maximal power and quality factor Quality factor: Quality factor is also a measure of the “sharpness” of resonance

  14. Lab 6: Forced Harmonic Motion • For each measurement allow enough time for the system to reach steady state after you changed the rotation speed.

  15. vmax peaks at 0 resonance

  16. How to measure phase? (Lock-in method) From data:

  17. How to measure phase? (Lock-in method) • Find out F0 and A; • Create a column with value Fx=F(t)x(t); • Sum over the column to find cos Here N is the total number of the data points

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