Changes

[[File:Cantilevers.jpg|200px|thumb|right|two diamonds and a rectangle]]

[[File:Cantilevers.jpg|200px|thumb|right|two diamonds and a rectangle]]

Step 1: Location of Resonance Frequencies

*Step 1: Location of Resonance Frequencies

Analysis was run in order to find the exact locations of the resonance frequencies for each individual cantilever. The cantilevers were mounted horizontally one at a time using a clamp to hold them fixed from one end. A microphone was set up near the tip of the cantilever, at an approximate distance of three centimeters away. The cantilever was then given a short, non-periodic impulse (a flick near the end) and allowed to settle into its natural oscillatory frequencies undisturbed. The microphone picked up the compressed air waves made by the cantilever’s vibration. This process was repeated three times for each cantilever. From this data the resonance frequencies were extracted using Fourier analysis.

Analysis was run in order to find the exact locations of the resonance frequencies for each individual cantilever. The cantilevers were mounted horizontally one at a time using a clamp to hold them fixed from one end. A microphone was set up near the tip of the cantilever, at an approximate distance of three centimeters away. The cantilever was then given a short, non-periodic impulse (a flick near the end) and allowed to settle into its natural oscillatory frequencies undisturbed. The microphone picked up the compressed air waves made by the cantilever’s vibration. This process was repeated three times for each cantilever. From this data the resonance frequencies were extracted using Fourier analysis.

[[File:FourierFrequencies.pdf]]

[[File:FourierFrequencies.pdf]]

[[File:Speaker_and_Cantilever.jpg|200px|thumb|right|the speaker and cantilever sharing a ring-stand]]

[[File:Speaker_and_Cantilever.jpg|200px|thumb|right|the speaker and cantilever sharing a ring-stand]]

Step 2: Measuring Relative Amplitude:

*Step 2: Measuring Relative Amplitude:

The optical lever technique was used to determine the relative amplitude of cantilever vibration at different points along the length. Each cantilever was mounted in the same fashion as before, and the clamp was attached to a ring stand. Also attached to the ring stand was another clamp holding a small speaker. Resonance was achieved by using the speaker to produce a constant sinusoidal output, which traveled through the ring stand to excite the cantilever. A class 111a laser pointer was mounted opposite the free end of the cantilever, pointing towards the fixed end. A white projection screen was mounted above the fixed end of the cantilever. In order to amplify the motion of the cantilever, which is normally very slight, the laser is reflected off the cantilever’s surface, and its own angle of motion is augmented by that of the cantilever relative to the horizontal at the point of reflection.

The optical lever technique was used to determine the relative amplitude of cantilever vibration at different points along the length. Each cantilever was mounted in the same fashion as before, and the clamp was attached to a ring stand. Also attached to the ring stand was another clamp holding a small speaker. Resonance was achieved by using the speaker to produce a constant sinusoidal output, which traveled through the ring stand to excite the cantilever. A class 111a laser pointer was mounted opposite the free end of the cantilever, pointing towards the fixed end. A white projection screen was mounted above the fixed end of the cantilever. In order to amplify the motion of the cantilever, which is normally very slight, the laser is reflected off the cantilever’s surface, and its own angle of motion is augmented by that of the cantilever relative to the horizontal at the point of reflection.