# Microcantilever Model Kit

#### (formerly the Dynamic Cantilever Kit)

#### Description

This kit support the Microcantilever Learning Module.

The Microcantilever Model Kit allows students to investigate the motion of a dynamic cantilever under varying masses and various dimensions in order to determine the relationship that expresses the resonant frequency of a cantilever as a function of mass or size. This activity simulates the dynamic mode of operation for microcantilevers used in MEMS sensors.

Students are required to produce a lab report based on their observations that contains the data collected, graphs created showing the relationship of two variables, and the experiment's results. The Microcantilever Model Kit contains cantilevers of different widths, thicknesses and materials. Clamps for mounting the cantilevers to a table, as well as "mass" objects are also included in the kit, along with the Microcantilever Learning Module – Book 1 and 2.

#### How can I use this kit?

One of the most basic structures used in MEMS is the cantilever. It forms the basis of RF (radio frequency) micro switches, certain types of chemical sensor arrays, and the atomic force microscope. Cantilevers also form various macro structures such as diving boards, balconies, tuning forks, and airplane wings.

Microcantilevers are used to measure the mass (concentration) of individual bacterium collected on a cantilever surface. This dynamic cantilever activity simulates this ability to measure small changes in mass, but at the macro-scale

In this activity students observe how does the width, thickness and length of a cantilever affect its natural frequency. In order to prove this affect, students record the cantilever's movements using a video camera and then analyze video data. What happens as you watch the vibration of a cantilever frame by frame? This is a great method to teach about position, velocity and acceleration vs. time (physics!). Students can even be taught the basics of calculus without them even knowing it!

Once the students acquire the video data, they learn to convert the frame by frame data to resonant frequency - a great hands on problem-solving activity by itself! Converting video observation to a spreadsheet graph of resonant frequency Vs Length, width, thickness, materials and mass added is a lot of fun.

Then - there is the theory! Analyzing and applying the "Mass on Spring" equation (algebra) to the data and extrapolating it to the micro-scale is enlightening. Students see that at this very small scale, using a material such as polycrystalline silicon, the natural frequency of a tiny cantilever is in the megahertz range! This too can be an "ah ha" moment. Now they have enough knowledge to design a cantilever to be ultra-sensitive.

So.... This is not just a **physics** experiment but ...

Music - how does a tuning fork work? Same concepts!

**Mathematics** - Measuring resonance as a function of cantilever length yields a non-linear result; one can acquire, plot data and then determine the unknowns in the equation - bulk modulus, and density of the material. Curve fitting anyone?

**Engineering and Materials Science** - How do the dimensions (L, W, T) affect the resonant frequency? What about stiffness (Bulk or Young's modulus)? How do you design a system that can measure individual e-coli cells and work with off the shelf electronics?

Science and Tech in general - **Data Acquisition and analysis** - This is so cool for most students because they love to "play" with their digital cameras. Some of the newer smart phones have high enough resolution and frame rate to record this activity. Students learn how to look at videos frame-by-frame and "see" what is going on. Taking this information and transforming it into a graph - wow! It should be noted that places like Sandia National Laboratories use high speed cameras to watch very fast events (like projectiles going through concrete) or Microsystems devices oscillating.

Cantilever-based **chemical sensors **are used in biotech as well as homeland security applications. Perhaps a BioTech course or Chemistry class can use this activity.

What else does SCME have for you? Well, we do have several **short animations and videos** which provide great supplemental information:

- "Save My Baby,"
- "Micro Cantilever Array,"
- "Cantilever Resonance Vs Mass Added," and
- "Frames per Second"

Plus lectures are available:

- "How Does a Cantilever Work?" and
- "MicroCantilever Applications Overview"