How would one go about finding the center of mass of a non-uniform rod when its cross-section has been modeling using a piecewise-defined function?
For a specific case let's use a drumstick, noting its volume as a sum of half of a sphere (the 'butt' end), a cylinder (the 'shaft'), the majority...
I really don't have much experience with calculus ( :sarcasm: Hooray! ), but earlier I was reading an introductory article explaining the usefulness of the Lagrange multiplier in dimensional optimization,
http://www.slimy.com/~steuard/teaching/tutorials/Lagrange.html
and it reminded me that...
Would it not be more efficient to write modular functions using the text formatting of logarithms? The modulus would be in subscript after "mod", and the expression to be used would be written after...
Ex. modnf(x)
Would it be possible to write an equation utilizing a summation of a modular function of a Cartesian function, whose degree is dependent upon the index of the root, in that it predicts the digits less than 1 of the root, that when summed equals the computed value sqrt( n )?
I already have what...
I've tried searching online for one in what I can only guess would be called a reduced algebraic form, and I cannot find it.
To make matters worse, for me, at least, I do not have the mathematics knowledge necessary to understand advanced functions, series, and transformations of mathematics...
I have been wanting to write an equation which predicts the tension on a circular membrane (AKA drumhead). However, I'm not sure that my answer is on the right kind of track, if it's even correct.
As for the procedures I took, first I started with the equation for tension on a string, which I...
As another of my personal music projects, I have wondered if it would not be possible to calculate the 'feel' of a drumhead (i.e. the amount of 'give' expressed as transverse displacement 'z' that an equally pre-tensioned circular membrane of radius 'r' experiences when struck on its plane at a...
Is it possible to predict the damping coefficient of a string using a mathematical simulation that included the string's diameter, length, frequency (and therefore tension), material density, and elastic modulus (if not also its Poisson's ratio) as opposed to simply looking at the amplitudes of...
I have put together an equation whose purpose is:
With a desired 'magnitude of static friction' ( μ_s ), 'fundamental frequency' ( f ), and 'tension' ( T ),
initial conditions such as 'string breakover angle' ( Θ_0 ), 'nut-tuner distance' ( L_{h,0} ), and 'string diameter' ( d ),
and...
At one point I had been trying to construct an equation which would calculate the tension on a tuned string with a change in temperature (and therefore the fundamental frequency), but found my calculations were wrong. By extension, the purpose of the project was to be able to calculate what...
In order for me to be able to run a simulation I need to write an equation which calculates the distance from a point inside a circle of radius 'r' to any point along the circle's circumference using a point a distance 0<=d<=r from its center. The ultimate system to be simulated is a radially...
As part of a personal musicology project I found myself with the mathematical model of a geometry which utilizes the equation
a*(a/b)sin(pi*x)
The only problem with this is that I need to take the integral from -1/2 <= x <= 1/2, and according to Wolfram Alpha no such integral exists. I can...
Working on a personal music project, I would like to pull 'z' out of the logarithm below if I can help it, but am having trouble:
It's a portion taken from this:
Which evolved from...
However, this is only the mathematical modeling of the object. The actual *physics* aspect...
Kinetic Energy of Double Compound Pendulum and Parallel Axis Theorem
Hello, there.
I have a project I'm working on where I need to be able to calculate the kinetic energy of what basically amounts a double compound pendulum. However, the pivot point of the second pendulum is not at the center...
I've been trying to write an equation for the tension of a string where a segment of the string is suspended between two points a set distance apart (the string extends beyond both points in both its initial and final conditions), and involves not only the periodicity of the string's movement...