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The reaction is a transformation. The rate law is
v=k[A] (first order in A, and first order overall). As you increase or
decrease the concentration of A by moving the slider the reaction
increases or decreases. The rate constant here is in inverse seconds
(s^-1 or hertz).
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R and B are reacting to form P. This rate law is
v=k[R][B] (first order in R and first order in B, second order
overall).
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One Y is reacting with two Bs to form one G. The rate
law is v=k[Y][B].
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The Amplitude-Frequency Plotter (AFPlotter) applet
allows the user to choose various values of the forcing frequency for
a certain selected natural frequency. The purpose of this activity is
to explore the relationships between both amplitude and frequency
(which is known as a Bode Plot), and phase angle and frequency.
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This applet calculates how wieghts on a balance will
fall, or not fall as the case may be. It takes into consideration the
weight, and distance from the fulcrum of the balance.
Keywords: |
Linked from: LinkedModulesGoHere
|
Programmers:
George Stockfisch, Seth Santos |
State:
beta |
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The Beats applet allows the user to explore the
behavior of the undamped forced spring mass system. By choosing the
forcing frequency, natural frequency, and amplitude, one can examine
the behavior of the system. In this particular case where the forcing
frequency is not equal to the natural frequency, this phenomenon,
known as beating, occurs and is illustrated by the applet.
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The Bicycle Frame Angle Analysis applet allows one to
understand how the vector dot product can be used to find angles
between two vectors. A position vector is created from each bicycle
tubular member and the angle between any two members is calculated via
the dot product and is displayed by the applet. Bike frame geometry
can be varied limitlessly by dragging the frame joints to new
positions. All the while the angles are continuously updated
permitting the student to perceive the relationship between geometry
and the dot product.
Keywords: |
Linked from: LinkedModulesGoHere
|
Programmers:
Dan Manthey, Shannon Pixley |
State:
beta |
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The Bicycle Pedal applet allows one to better
understand how moments (torques) develop and are useful by examining
their role in pedaling a bicycle. The user can move the bicycle pedal
and crank to any position in a normal cycle and apply forces. The
resulting torque is displayed on the pedal. Data from several
positions can be used to animate the pedal or the pedal can be
animated from experimental pedaling data. The numerical values of all
forces and moments and their components can be displayed as well as
plotted versus crank angle.
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The Bicycle Pedal applet allows one to better
understand how moments (torques) develop and are useful by examining
their role in pedaling a bicycle. The user can move the bicycle pedal
and crank to any position in a normal cycle and apply forces. The
resulting torque is displayed on the pedal. Data from several
positions can be used to animate the pedal or the pedal can be
animated from experimental pedaling data. The numerical values of all
forces and moments and their components can be displayed as well as
plotted versus crank angle.
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The Budget Optimization Applet allows you to animate
a level curve, which corresponds to the production level, as
constrained to a budget line. A production level meter indicates
relative production levels achieved at any given point along the
budget line. Illustrates the concept that a maximal production level
occurs when the level curve is tangent to the constraint.
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Introduces a functionally infinite volume sink
separated from the single chamber by a semi-permeable membrane. The
user selects the permeability of the membrane and the initial
concentration of solute in the single chamber. Then the applet plots
the concentration of solute in the single chamber over time as it
decreases due to the presence of the sink.
The applet takes in as parameters:
TimeStep: Used in the First Order Non-Coupled Differential Equation as delta_T (given as a float)
NumContainers: Deligates how many buckets the program is going to look for (given as an integer)
C_i:Each bucket, where i corresponds to the current and unique bucket number.
The vaue tag contains a string delimited by ','(commas) as follows:
Initial Volume: An inital volume for that current bucket. If the volume is -1.0, that bucket is said
to be infinite in volume. Given as a float.
Initial Mass: The initial mass of the dye in the dye bucket. If the volume is -1.0, this value is ignored. Given as a float
Plot Color: The color you want to represent this bucket in the plot. Given as a pre-defined Java Color.
Keywords: |
Linked from: LinkedModulesGoHere
|
Programmers:
Frank McDermott, George Stockfisch, Christopher Parker |
State:
alpha |
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This applet demonstrates how chemical equilibruim will shift from left to right depending on the concentration of each component of the reaction I2 + H2 --> 2HI.
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This applet demonstrates probability in the form of a coin toss. The user has the choice of tossing one to three coins and the odds of heads, tails, or a combination of the two on various coins is displayed. The user is also offered PMF and CDF plots to further demonstrate the probabilities of outcomes.
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Below is an interactive illustration with two parallel plates of area A, separated by a distance d and containing two conducting materials. You can vary the amounts of each material by clicking on the resistor; the dividing line jumps to where you clicked. You can change their resistivities with the choosers labeled "rho1" and "rho2". Choosing "Inf" gives the material infinite resistivity, that is, it becomes a perfect insulator.
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This applet demonstrates calculating conditional probability using an example of differentiating defective computer chips from good ones and representing the results in various histograms.
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This applet demonstrates an example of a small business in the context on constrained optimization. The goal is to find the maximum production level achieved within a given budget, and the budget's distribution of funds between labor and equipment. The user drags the production function around on top of the budget constraint line and determines when production reaches it's maximum by referring to a bar measuring it.
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This applet demonstrates the uniform, normal, or exponential distribution of continuous random variables. It takes minimum, maximum and the number of points from the user and plots the probability distribution function and the cummulative distribution function.
Keywords: |
Linked from: LinkedModulesGoHere
|
Programmers:
Mark Watson, Shannon Pixley |
State:
beta |
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The contour applet asks the user to draw the vector of the contour at 3 points. The user then presses the answer button, and the correct vectors are displayed.
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This very simple applet presents images of graphs and
prompts the user to venture a guess as to whether they are actually
different representations of the same graph. The purpose of the applet
is to demonstrate that graphs that look very different may in
actuality be "the same" (isomorphic).
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This applet demonstrates the effects of variation of lambda on poisson distribution and the frequency of occurence of certain values.
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This applet displays objects falling based on the falling medium. It calculates and graphs the velocity and acceleration of each object and allows the user to compare the speeds and accelerations of the two objects.
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This applet demonstrates a drilling scheme proposed
in the Graph Theory | Industrial Drilling module. The module user is
able to examine the succession of drilling on a click-per-step basis,
or view a threaded animation of the entire drilling process.
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This applet demonstrates the role average daily demand plays in average daily cost and percent losses in an inventory control problem. It shows the results in the form of a scattergram, fixed order point, or fixed order size.
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The Eyemount applet shows force vectors applied to an
eyemount as a demonstration of the fundamentals of vector mathematics.
Any number of force vectors, represented by their magnitude and
direction or their Cartesian components, can be applied to an
eyemount. The resultant vector, found by vector addition, and its
components can be calculated and displayed. The user can choose
between no axes, conventional horizontal-vertical x and y axes or x
and y axes with a second set of axes which can be rotated at any angle
with respect to the x and y axes. This set of axes allows one to see
the variable nature of components as the axes with respect to which
they are defined change.
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The electric and magnetic field applets use every possible combination of mouse buttons and modifier keys (these are sometimes called chords) to do interesting things. There are too many of them to list in each module, so the complete list is here (http://links.math.rpi.edu/devmodules/electricpotential/html/fieldchords.html) for easy reference. Applet demonstrates properties of point particles.
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This applet simulates the electric field of positively and negatively charged point particles and demonstrates their field lines as they interact with one another.
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The Forced Spring Mass applet uses the analytical
solution of the motion to predict the behavior of the system. In this
applet, the user can change various parameters, including the mass,
spring constant, and forcing frequency, to examine how the behavior of
the system is affected by changing certain model
parameters.
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This applet demonstrates the sound waves of undamped vibrating strings on a graph. The user clicks the buttons at the bottom of the applet to superimpose different sinusoidal functions. Once the user is familiar with the way these functions interact, the user tries one of the three "test your skills" buttons. G(x) made up of the four sinusoidal functions are provided here and the task is to remove components until the gets a constant zero function.
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This applet is a follow up to fourier-series-trog. It allows the user to select the amplitude base from a more continuous range of values and play the resulting sound. Ultimately the student will learn to calculate the amplitude using Fourier series instead of using these trial and error methods.
Keywords: |
Linked from: LinkedModulesGoHere
|
Programmers:
Mike Malak, Angela Graveline |
State:
alpha |
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The Free Body Diagram applet takes the student
through all of the steps of idealizing a physical system to create a
free body diagram (FBD). The applet guides the student through a
series of questions which asks the students to make choices about
which types of forces to apply and prompts him/her to choose to
correct location on the diagram. In this manner students can
methodically dissect a system into three workable free body diagrams
which could be used to solve for the reaction forces of interest in
the problem.
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This applet simulates the output of Geiger counter sounds. It then demonstrates how the sounds follows a Poissen distribution. The user must view the output and mark the events to estimate lambda.
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This applet makes use of the package
links.applet.graph to display a graph and run an animation of the
progression of a specified algorithm on that graph. Javadoc
documentation of the links.applet.graph package, which allows for
creation of both logical and visual representations of graphs, is
available. The purpose of the applet is to demonstrate the operation
of various algorithms an different graphs.
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This applet makes the mathematical formulas displayable in the graph isomorphism module.
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This applet simulates heat flow between two boundaries with different controlled levels of heat which are determined by the user.
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The Image Magnification Applet allows you to display
one of several pre-programmed images, and then click to "zoom in" and
see the pixels that make up the digital image. On the last click, the
applet displays the gray level values on top of each pixel.
Illustrates that digital images are made up of much smaller elements
called pixels.
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The Image Noise Applet allows you to display one of
several pre-programmed images, and then add uniform or Gaussian noise
to the image. You can compare visually the effects of adding noise to
images. The original image is displayed in a separate window for
side-by-side comparison with the "noisy" image.
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This applet shows the user an EMF reading as various parts of a plain bar magnet pass under a reader.
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This applet demonstrates how an integral's measures of area under the curve and centroid become increasingly accurate as the slices sampled get progressively smaller and more numerous in size.
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This applet demonstrates various types of lines. It allows the user to add, move, or delete a point on the line. They are given the of line types that are linear, cubic spline, newton, and spline.
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This applet allows the user to explore the magnetic field of a current carrying wire.
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The user is given a choice of level curve, gradient, surface, and formula, and has to match the two sides. A window pops up and tells the student if their guess is correct.
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This applet helps the user explore 2 x 2 matrices.
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This applet demonstrates how to find the inverse of a two-by-two matrix. If matrix A is given, and the user knows that AxB = I, then this applet will help the user solve for B.
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This applet shows the user how to multiply two matrices. The user can select any dimensions from 1-4 four times to dictate the size of the matrix, and the applet displays the product of the matrices entered.
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This applet allows the user to rotate a vector by either entering in new x-y coordinates or a new angle. The applet returns the tranformed x-y coordinates.
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This applet allows you to explore the application of
linear algebra to the analysis of mechanical systems with two degrees
of freedom.
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The Mountain Biker Weight applet demonstrates how the
weight of a mountain biker varies depending on the height of the
mountain he is biking on, according to Newton's Law of Universal
Gravitation. The mountain biker's mass and eventual mountain height
can be varied while his weight is plotted as a function of altitude as
he ascends the mountain. The affects of smaller and larger planetary
masses and radii are demonstrated by choosing to mountain bike on
several different planets or the moon.
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This applet demonstrates multiple matrix transformations on a 2-d plane. The user can add or delete additional matrices.
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The Navigation Chart Applet simulates a navigation
chart and tools that ship captains might use in order to navigate
their ships. It allows you to use a compass to draw circles and a
ruler to draw lines in order to navigate to the closest shore
position. A relative distance meter enables you to estimate
ship-to-shore distances. The objective is to explore a specific
application of constrained optimization: a ship's optimal navigation
path when constrained to a shoreline.
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The Navigation Optimization Applet allows you to view
the relative distance from ship to shore via a line drawn from ship to
shore and a relative distance meter. At each point along the
shoreline, the local normal to the shore is also shown. Illustrates
the concept that a minimal distance occurs when the local normal to
the constraint is aligned with the minimum distance to
shore.
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The user specifies the initial velocity and pendulum length, and then presses the
kick button. In the left window the phase plane, corresponding to this particular choice of initial
velocity, is displayed with a plot of velocity versus theta. The right window
contains a graphical display of the index of the equilibrium point versus the initial velocity.
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This applet demonstrates how a candle appears when it goes through a convex or concave lens, or both.
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This applet allows the user to see the change in accuracy for measuring the full signal's energy depending on number of oscillators used in this equation from zero to infinity (integration).
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This applet allows the user to enter the length of the rod, mass of bob, initial angular velocity and initial angle. It then animates the pendulum's motion and plots displacement and angular velocity versus time and angular velocity versus displacement.
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This applet simulates nonlinearity of the mathematical model of this module. The user specifies the pendulum length and starting angle. They then press the "get period" button, which displays the movement of the pendulum in theta versus time. The user then has the option of displaying period versus initial angle in a graph.
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The Piston Applet allows you to vary the volume of
gas inside a piston and observe the corresponding change in
temperature.
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The Regression Analysis Applet allows you to plot a
line based on its equation and then add uniform or Gaussian noise to
the data points. The applet determines the best fit of a line to the
"noisy" data points. Illustrates how noise affects data.
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This applet simulates a RLC circuit. The user sets the resistance, inductance and capacitance and the time frame, and the applet displays graphs of the voltages, current, and charge.
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This applet helps the student investigate the effect of noise on binary signals. Specifically, it has the user walk through this with an example ofa burglar alarm and responding to false versus real alarms.
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This applet demonstrates a sound wave with it's unknown base amplitude at various points multiplied by +1, 0, or -1. The student is then allowed to play the resulting sound wave.
Keywords: |
Linked from: LinkedModulesGoHere
|
Programmers:
Mike Malak, Angela Graveline |
State:
alpha |
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This applet allows the user to see how angle and field strength affect flux. The user sets two angles, theta and phi. The applet then plots flux versus angle.
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The Simple Uniform Flux applet shows a closed, planar
loop in a vector field that may represent the flow of water. The
inclination of the loop can be varied in both the theta and phi
directions, the viewing angle can be manipulated to gain a better
perspective of the system, and the field strength may be modified as
well. The projected area of the loop normal to the flow direction is
also displayed (both visually and numerically). Students can use the
applet to see what characteristics of the loop affect the flow rate
through the loop. The applet also provides the ability to plot the
flux through the loop versus the angle theta, phi, or both, allowing
the student to discover that the flux depends on the area, and has
cosine dependence upon the angle of orientation. They should also come
to understand that it is the projected area that
matters.
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The Sine + Cosine Applet allows users to plot a sine
wave and a cosine wave on the same set of axes, and then provides the
opportunity for the user to guess the sum of the two by "drawing" on
the screen with the mouse. The user has the ability to show the
correct sum of the sine and cosine waves.
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Reviews the simple case of mixing one solute (mass)
source and one solvent source inside a single container. The mass of
solute and volume of solvent are user selected and are subsequently
mixed in the single chamber. The applet calculates the concentration
of solute in the solvent and plots it on a graph. Instantaneous mixing
is assumed.
Keywords: |
Linked from: LinkedModulesGoHere
|
Programmers:
Frank McDermott, George Stockfisch, Christopher Parker |
State:
alpha |
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This applet demonstrates how two different skiers taking different initial angles on a hill while "skiing the fall line" (see gradient module) will take varying times to get down the hill. A second part of the applet traces the line each skier takes in their descent down the hill.
Keywords: |
Linked from: LinkedModulesGoHere
|
Programmers:
Luke Bellandi, Jeffrey E. Care |
State:
beta |
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Simulation of a skydiver (or, optionally, a sphere)
falling in air. User controls parameters such as mass of the skydiver,
height of the drop, and drag coefficient. As the skydiver falls, his
velocity and acceleration are plotted against height. Optionally, the
applet can be instructed to show the object reaching terminal
velocity.
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This applet simulates a sky diver falling and plots acceleration and velocity versus time during the fall.
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Snell's Law applet demonstrates the law for a variety of surfaces on both sides including air, a vacuum, water, etc.. The user clicks where the light should come from, and the angles of reflection and incidence are displayed visually.
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This applet provides a graphical interface through
which a user can begin to convince herself that Sperner's Lemma really
does hold.
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This simulates a sphere of 1 nC, uniformly distributed throughout the it. The sphere has a radius of 100 mm. The user stretches the radius of the sphere, and the corresponding charge enclosed (in v/M) is displayed with the diameter.
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This applet pops up with a simple spreadsheet. It has the addition and equal functions and shows the user how to enter simple values and add cells together. Has issues.
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The Spring Mass Applet enables the user to select
parameter values (spring constant, damping coefficient, and mass) and
initial data (position and velocity), and then to observe an animation
of the corresponding spring-mass system. Outputs are graphs of
position versus time, velocity versus time, and velocity versus
position. Both damped and undamped systems are included in the
applet.
Keywords: |
Linked from: LinkedModulesGoHere
|
Programmers:
Matt Kost, Dan Manthey, Dave Cooper, Teera Fa-Gon |
State:
beta |
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This model demonstrates how a spring pendulum works. The student sets the angle of release, length, distance and k and the pendulum oscillates on the screen. The applet then plots r versus theta and theta and r versus time.
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This applet shows the two dimensional spring pendulum: a mass suspended on a spring. The pendulum moves under the influence of gravity and the elastic force of the spring. One can drag the pendulum to it's starting position.
Once in motion, the pendulum can be 'caught' by clicking and holding the mass.
Keywords: |
Linked from: LinkedModulesGoHere
|
Programmers:
Sergey Kiselev, Tanya Yanovsky-Kiselev |
State:
alpha |
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This applet demonstrates how to stretch a vector. The user is allowed to visually "stretch" the vector on a 2-d plane with the mouse, grabbing the blue dot. When the update A button is pressed, or auto is checked, a matrix with the adjustment is displayed. Eigen values and Eigen vectors are also displayed.
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This applet demonstrates how to multiply two matrices. It is assumed the matrices are of the same size.
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Builds upon the Single Chamber case by adding a
second primary mixing container and a secondary mixing container. The
contents of each primary mixing container, having one solute and
solvent source, are mixed and then their contents are mixed in the
secondary mixing chamber. The applet calculates the concentration of
solute in each container and plots it on a graph.
Keywords: |
Linked from: LinkedModulesGoHere
|
Programmers:
Frank McDermott, George Stockfisch, Christopher Parker |
State:
alpha |
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This applet demonstrates how to transform a point using a 2x2 matrix. The user enters the first point, and adjusts the matrix. The second point reflects the matrix transformation.
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This applet uses a 2x2 matrix to transform a rectangle. The user may adjust the starting points on the rectangle and modify the transformational matrix. The 2-d graph adjusts itself appropriately and displays the coordinates of the transformed rectangle next to it.
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The applet below will help you get a better feel for the direction of the gradient in relation to
three-dimensional graphs and level curves.
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The user may click the buttons at the bottom of the applet to superimpose (add together) different sinusoidal functions. Once they are familiar with the way these functions interact, three "test your skills" buttons are available. G(x) will be given and is made up of the four sinusoidal functions available here and your task is to remove components until you get a constant zero function.
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The Weight Distribution to Bicycle Tires applet simulates what would happen if you sat on a bicycle and put a scale beneath either tire. As the bicycle rider shifts positions on the bike, from leaning on the handlebars to sitting back, the weight is distributed differently between the two tires. The user inputs weights on the handlebar, pedal and seats, and the weight on each tire is displayed appropriately.
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The user is presented with a two dimensional graphic
of a delta wing, viewed from the top and the bottom, with an
appropriate discrete pressure function shown, both visually and
numerically, on the wing. The user has the ability to modify the
refinement of the discrete pressure function and see the effect that
their modifications have on the overall pressure above and below the
wing. This leads the student from the notion of a discrete sum to that
of a surface integral.
Keywords: |
Linked from: LinkedModulesGoHere
|
Programmers:
Dan Manthey, Christopher Parker |
State:
beta |
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When the show buttons for x=1, 4, 9 are depressed, the isotherms (contour curves) are displayed on the graph. The "answer" button displays the heat flux vectors at the given points. This applet allows students to check their work on problems 20-22 on the heat flow module.
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