This project uses an electronic circuit to demonstrate something called stochastic resonance. Stochastic resonance (SR) is present many places in nature–from dictating the timing of ice ages to aiding in fish hearing. So, what is it? SR is simply when a random noise signal serves to boost the strength of another, cleaner signal. Audio is a good way to think about this. Imagine you are listening to a song, but the volume is so low that you cannot hear it. Then you add another speaker playing random noise. You start to turn up the noise, and at a certain point, you start to hear the song. This is pretty strange, and quite counterintuitive. Usually adding noise drowns out other sound, so how could random noise serve to boost a sound? This project seeks to examine that question by observing stochastic resonance in a circuit. Every signal running through the wires I used could easily be sent to a speaker and played aloud, as all of the frequencies involved are within the auditory range.
The circuit used here is called a Schmitt trigger. Its purpose here is to allow a signal to pass through if it is strong enough, but block weaker signals. The point at which the signal is strong enough to pass through the Schmitt trigger is called the threshold voltage. One other side effect of the Schmitt trigger is that the output signal will be a square wave rather than a sine wave. I ran a strong signal through at first to confirm that the circuit was operating as it should, then I ran a weak signal through and saw that the output disappeared. At this point, we have a weak signal entering the circuit, but no output, just like when you were playing a song, but it was too weak of a signal for your ear to register. So, I then added random noise to my signal. The random noise makes the input sign wave cover a larger range of voltages, puncturing the threshold voltage, and once again allowing the circuit to output a square wave. This is stochastic resonance in a hysteretic circuit.
Using this circuit I was able to determine the best possible noise volume to cause SR in the given parameters. The circuit itself could be used to make a hearing aid that listens for cleaner weak signals and filters out excess noise. This circuit is also interesting as a metaphor for other things in nature, as it behaves similarly to the human neuron.
The purpose of my experiment was to analyze whether the behavior of an RLC (Resistor, Inductor, Capacitor) circuit is noticeably affected by replacing the inductor with an oscillating spring. Common inductors take the form of solenoids which are helical coils of wire that are wrapped around a core. This core can be made of different materials, but some of the more common are ferromagnetic materials like iron, cobalt, or nickel. The core can also just be air, which is similar to the model that the spring mimics.
When a current starts to run through an inductor, the inductor resists the current. After a brief period of time, the inductor will no longer resist the current and the system is in equilibrium. If the current changes, however, the system will no longer be in equilibrium and the inductor will once again try to resist the change. In order for the inductor to resist the change, there must be some sort of force that it applies to the current. It turns out that this force is exerted through the use of a magnetic field acting on the current. Therefore, we say that if the current changes, it induces a magnetic field that resists the change in the current. This is a reciprocal relationship, too. If instead, the magnetic flux (the amount of magnetic field flowing through the area of the inductor) changes, then a current will be induced that opposes the changing flux.
By exploiting this trait of inductors, my hope was to see significant change in the output voltage of my circuit. For an RLC circuit, the output voltage is dependent on the frequency that is driving the circuit. For certain frequencies, the output voltage will be approximately zero, whereas for other frequencies, the output voltage will be immense. The curve on a graph of output voltage as a function of frequency is called the resonance curve and the maxima of this curve is referred to as the resonant frequency. The width of the curve as well as the location of the resonant frequency are dictated by the inductance in the circuit. The inductance of an inductor is dependent on some of its geometrical properties such as its length and radius. Therefore, with a spring, the geometry can be altered and inductance can be actively changed as the circuit is running.
When I placed the spring in the circuit, I was able to observe the resonant frequency shifting to different values by stretching or compressing it. For one trial, a mass was suspended from the spring and the mass/spring system was made to oscillate. During the period of oscillation, the inductance of the spring was constantly changing which meant the inductor was continuously responding to changes in current and magnetic flux and resisting them accordingly. While observing the electrical, sinusoidal signal passing through the circuit on an oscilloscope, I could actually see the amplitude of the signal changing corresponding to movement of the spring. See attached video in order to watch this phenomenon.
For my Junior Independent Study, I looked into some cool physics videos to find an interesting topic to explore. I found a youtube video about the University of New Mexico Couette cell apparatus for demonstrating laminar flow and decided that watching fluid blend together and then separate out again was an interesting concept. The project I designed was to bring this apparatus to the College of Wooster and then experiment with it. I looked into how accurately a line of color could be returned to its original location after being rotated at various angular velocities and if the transition was more accurate at varying depths below the surface of the fluid.
Walking – we all do it. But why do we walk so often? Why doesn’t everyone skip down the block to work?
Aside from that being deemed as weird by society, walking is the most efficient way for people to move on earth due the gravity here. We’ve all experienced this in some way. You probably know that it’s much easier to walk long distances, than to run them. In my Clare Boothe Luce work this year, I confirmed that walking is amazingly efficient by simulating a passive walker that is able to walk down a hill simply through the force of gravity.
My Junior IS study “Building a Passive Robot for Active Learning,” aimed to take this simulation research and create a real passive walking robot (a robot without a motor) out of plastic Tinkertoys. I used a previous study done by a group at Cornell to base my walker design off of and to use as a comparison. When they built their robot in the 1990s, wooden Tinkertoys were mass-produced, but now plastic Tinkertoys are the only financially possible option. I found that the walkers behaved slightly differently due to sensitivity to initial conditions and parameters for passive walkers. Though this difference exists, I proved that it is still possible to create this simple passive walking robot.
The hope is that this walker could be used as an outreach tool at Science Days at the College of Wooster in order to introduce kids to engineering and to make mechanics a more approachable topic to them. This project is a fun way to spark children’s imaginations and learn more about how fascinatingly efficient human movement can be.
This spring, each Wooster Junior physics major undertook a six-week scientific investigation of their own design, as a part of our junior independent study course. Watching their projects come to fruition over the course of the semester was a very rewarding experience for me, and I am happy to announce that each junior prepared a blog post on their project. These will be posted shortly as a series of guest blogs, so please stay tuned!
The tallest structure in the world since 2008, Burj Khalifa (or Khalifa Tower) is the fantasy skyscraper of my childhood. Designed by Skidmore, Owings & Merrill (SOM), with Adrian Smith and Bill Baker as chief architect and engineer, the Burj is aesthetically and structurally magnificent. No single photo can do the Burj justice, but the one below emphasizes the Y-shaped floor geometry that buttresses the central core and the complex spiral pattern of 27 setbacks that decrease the cross section. Crucially, the terraces “confuse the wind” to minimize vortex shedding vibrations, the bane of skyscraper designers.
Over a half-mile high, Burj Khalifa is the world’s tallest building. Photo by Stéphane Compoint.
Giant bowl of veggies, waiting to be grilled
Last weekend we had another excellent picnic and pie festival at my house. This event has been a tradition since my first summer in our REU program back in 2004. We have outdoor games, eat grilled veggie quesadillas and a variety of sides, and then we have the celebration of pie!
This year’s pie festival happened to fall on the 22nd of July, or 22/7 if you write the date in a European date/month format, or “European pi day” as Dr. Lindner likes to call it. Pi is of course an irrational number and thus cannot be represented by a fraction like 22/7, but it turns out that 22/7 is a reasonably good approximation of pi and has been widely used to simplify calculations, and so holding the pie festival on pi day is particularly sweet.
Fast-paced, no-net badminton! The birdie (bright blue) can be seen in the upper left of the photo.
KanJam action shot
Frisbee in flight!
This year, we had a great assortment of pies, including pecan pie, strawberry-brownie pie, raspberry blueberry tart, chocolate peanut butter pie, pineapple pistachio pie, peach cream pie, sour cherry pie, and shoo-fly pie! I always make several pies (three this year), but the students contribute the rest!
Whew! I think we did have one noble soul attempt to take a slice of all the pies, but I believe he later regretted it. Of the pies that I had the room to try, the pineapple pistachio was my favorite because I hadn’t had a pie like it before, but they were all good!
A delicious assortment of pies!