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

A constant energy flow at steady state

Forced harmonic oscillation (steady state)

Forced harmonic oscillation (cont.)

Amplitude of displacement: Amplitude of velocity:

Amplitude peaks at  0  resonance

v max peaks at  0  resonance

Phase changes sharply at resonance

Forced harmonic oscillation (log scale)

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

Energy that flows out (dissipation) The power P dissipated by F d is: The average over one cycle is

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

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

v max peaks at  0  resonance

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

How to measure phase? (Lock-in method) Find out F 0 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