Curve Definition and 1000 Threads

Please see attached illustration (from Discover September 2004. Einstein 100 years special issue). Is it correct that one key to Einstein's thinking is to analyze a spnning disk. That "Since the rim of the disk travels faster than the center of the disk, the theory of relativity states that the...

Hi, consider the following curve: f(\theta) = \frac {I_0sin^2(n\theta/2)}{sin^2(\theta/2)} When the area over a cycle from ##0## to ##2π## is evaluated it gives ##(2πnI_0)##. This is exactly ##\frac {I_{max} + I_{min}}{2}## , since ##I_{min}## is ##0##. Is this a coincidence, or is...

I only need help with how to find the component of gravity along the curve. See image.

I would like to use a known area and values on the x-axis to generate a gamma curve to obtain y values. Please point me in the right direction. A = 0.07 m^2 Values on x axis 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.3 1.4 1.5 1.6 1.7 Thank you!

Hello guys (and girls), I'm trying to determine the dark phase of a type Ia supernovae. In order to do that I need to calculate the photosphere's velocity. So I'm trying to determine the redshift of the Si II in the spectra, by finding the minima in the absorption line. But what kind of...

I am trying to develop an equation or algorithm to determine the roulette curve that results from rolling a curve over another fixed curve. A general method to determine the roulette using any two curves, rolling and fixed, seems to be presented here...

Homework Statement Use Desmos to graph the spiral ##r=\theta## on the interval ##0\leq\theta\leq4\pi##, and then determine the exact length of the curve and a four decimal approximation. Hint: ##\int \sec^3(x)dx=\frac{1}{2}\sec(x)tan(x)+\frac{1}{2}\ln\left|\sec(x)+\tan(x)\right|+C## Homework...

COD stands for co-ordinate. As the title says, you have two co-ordinates of a point, x and y, on a unit square. What's the formula for converting these two co-ordinates into a single Hilbert curve co-ordinate? Which represents the percentile along the length of the Hilbert Curve that point is on.

<Moderator's note: Member has been informed to separate different question into different threads in the future.> 1. Homework Statement Please see picture attached... The diagram shows the curve with equation y = f (x) The coordinates of the minimum point of the curve are (–2, –1) (a) Write...

Homework Statement Homework EquationsThe Attempt at a Solution I don’t have a clue on how to do the calculations. I know the equivalency point is at the steepest part of the derivative graph. Please don’t say just figure it out, I truly need help. I haven’t learned titrations in lecture yet...

Recently I have studied that from the rotation curve of spiral galaxies, the nearly constt. behaviour of velocity of the stars situated far away from the central core suggests mass(r) ~ r ,rather than 1/√r as expected. Are there any other theory which proves the existence of dark energy ??

In 2-D Cartesian coordinate system let's there exist a scaler field Φ(x1,x2) ,now we want to find how Φ changes with a curve which is described by the parameter(arc length) s dΦ/ds=(∂Φ/∂xi)dxi/ds Can we say for Cartesian coordinate system that along the curve at any s dxi always points in the...

Homework Statement I have to find length of the curve: y2 = (x-1)3 from (1,0) to (2,1) Homework Equations s = ∫ √(1 + (f '(x) )2 ) dx where we have integral from a to b The Attempt at a Solution I'm bit confused: I'm thinking of writing function regarding x, f(x)...

I'd like to plot a Bragg curve for an alpha particle in air. I'd like to make one plot for 239Pu (5.156 MeV alpha) and one plot for 238U (4.267 MeV). Does anyone know how I can do this? I would like a basic plot of stopping power (MeV/cm) vs path length (cm). Thank you

Hi all I was wondering if someone could help explain what the area under a load vs deflection curve tells you. I have a concrete sample which I loaded until it failed. I plotted the load (kN) and deflection (mm) as shown below. My question is; if the curve in red can be represented as a...

Homework Statement Let ##U## be a plane given by ##\frac{x^2}{2}-z=0## Find the curve with the shortest path on ##U## between the points ##A(-1,0,\frac{1}{2})## and ##B(1,1,\frac{1}{2})## I have a question regarding the answer we got in class. Homework Equations Euler-Lagrange ##L(y)=\int...

is it possible to draw a random curve on a piece of graph paper and find the function that defines that curve? Assuming smooth curves. And if so,is it possible to do so with complex curves? tex

I drew a diagram in order to help figure out something for a tabletop game I'm putting together. My question is about the physics of materials, and is not directly about the fictitious psychic/magic abilities in my game world. I drew a diagram consisting of dots representing particles and...

Hi people, I am looking for a database where I can get raw data to plot the Bragg's curve for alpha particles energy loss vs range in Silicon, Germanium and CZT. Your help will be much appreciated. Cheers, Shri

Homework Statement Parameterize the part of the curve which allows an equilateral triangle, with the height 3R, to roll from one vertex to the next one, while its center travels at a constant height. Homework Equations I will include some pictures to show what I'm doing The Attempt at a...

Please see attached image. When we want to find the area under a curve, we can use the formula ##A = \int_a^b\left|g(x)-f(x)\right|dx## where g(x) is greater than f(x) and both are continuous over the closed interval ##[a,b]## My text, as seen in the picture, described the area under the curve...

I know that scanning tunneling microscopy (STM) I-V curve is exponential for a conducting sample. How would it look like if I had a semiconductor and a non-conductor sample?

May I know how to solve the equation as below: (1) y2 = x3 + x + 1 mod 17 Finding Inverses Finding Points on the Curve (2) y2 = x3 + 3x + 1 mod 13 Finding Inverses Finding Points on the Curve

Please help in the explanation of BH curve (See attached file). At the starting point, more current is required to bring the material to its magnetic saturation point( in fig form origin to pt.a shown by purple line ) as compared to when the material is fully demagnetized and then brought to...

Homework Statement Write the equations of tangent lines to the curve of the implicit function x2+2x+2y2-4y=5 that are normal to the line y=x+122. The attempt at a solution I know that the slope has to be m=-1 I found the derivative using implicit differentiation: dy/dx=(-2x-2)/(4y-4) Now I am...

Homework Statement If I have the two curves ##\phi (t) = ( \cos t , \sin t ) ## with ## t \in [0, 2\pi]## ##\psi(s) = ( \sin 2s , \cos 2s ) ## with ## s \in [\frac{\pi}{4} , \frac{5 \pi}{4} ] ## My textbook says that they are equivalent because ##\psi(s) = \phi \circ g^{-1}(s) ## where ##...

Homework Statement I need to obtain the equation of 2 paraboloids separated by a distance L. Homework Equations I think that the equations should be: z_1=x^2+y^2 z_2=x^2+y^2-L The Attempt at a Solution The problem is that when I plot the region between two inequations, x^2+y^2>=z and...

I am very new too Matlab and how it all works but I am having trouble understanding at what axis the numerical integration is occurring from on the graph that I plotted. So I am currently doing an experiment in gamma ray spectroscopy and due to issue with the software we found it hard to...

Hi all I was hoping someone could shed some light on the following:- I am trying to understand what Yield strength is and understand the exact limit of where elastic and plastic deformation occurs on a stress strain curve. Correct me if I am wrong but I define:- Yield strength as the amount...

Hi, I'm stuck on a homework problem in my Calculus III class. I solved 3a really easily, but 3b is giving me a lot of trouble. I know that to find the tangent line, I first have to find the slope, which is represented by the vector: <3cos^2(t)(-sin(t)), 3sin^2(t)(cos(t))>. I know the formula...

Homework Statement A car rounds a level curve of radius 100 meters at a constant speed of 30 m/s. What is the magnitude of the acceleration of the car? Homework Equations C = 2piRThe Attempt at a Solution I calculated the circumference as 628m. Besides that, I'm ignorant of the procedure to...

Homework Statement Variables are all given as arbitrary constants Homework Equations W=∫F⋅dl y=½bx^2 μ=cx^2 The Attempt at a Solution The obvious force action on the object is the downward gravity force. I don't see how to calculate the force that 'moves' the object down the curve or the...

When two magnets already sticked to each other being pulled apart, energy is applied, so I assume that the energy is stored like some sort of potential energy which will be turned back into kinetic energy when they accelerate towards each other to stick back together. So the magnet itself...

Homework Statement The graph of ##y^2 + 2xy + 40 \mid x \mid =400## divides the plane into regions. The area of the bounded region is? Homework Equations All relevant to calculus The Attempt at a Solution My question is how to predict the graph without using a grapher here? I put x and y=0 to...

Homework Statement f f Homework Equations ##a = {v^2}{r}## ##d = vt## The Attempt at a Solution The way I do it is break it down into the curved and straight segment. The bicycle is always traveling at a constant speed. Curved portion: distance ##\frac{\pi R^2}{4}## acceleration ##=...

Hello. The curve y = x2 is a parabola that looks like this: I have a shape Square that looks like this: What I am noticing is that if I consider the equation y = x2 and also the shape Square, I find that there is no connection between them but the equation y = x2 is pronounced as x-square...

For my understanding there should be no big difference in i-v curve between regular p-n junction and p-i-n junction, the only difference i can think about is do to the bigger resistance of the intrinsic layer. The curve should look the same only the current will rise little bit slower, because...

How can i calculate transfer function of curve? for example from time response of a curve. or transfer function of ferquency response .

Hi, The main question revolves around the Rhodonea curve AKA rose curve. The polar equation given for the curve is r=cos(k). The parametric equation is = cos(k(theta)) cos (theta), = cos(k(theta)) sin(theta) . Can anyone show me the conversion from the general parametric form to the general...

Can anyone recommend papers that directly curve-fit redshift as a function of luminosity distance for type Ia supernova and gamma ray bursts? I am looking for papers that do not curve-fit the data via an assumed model, even one as simple as Friedmann–Lemaître–Robertson–Walker (FLRW) metric. I...

Homework Statement Find the length of the curve: ##x=\frac{t}{1+t}## ##y=\ln(1+t)## where ##0 \leq t \leq 2## Length of curve integral ##\int^a_b \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2} dt## Homework Equations ##(\frac{dx}{dt})^2 = \frac{1}{(1+t)^4}## ##(\frac{dy}{dt})^2 =...

Let $$\phi(x^1,x^2...,x^n) =c$$ be a surface. What is unit Normal to the surface? I know how to find equation of normal to a surface. It is given by: $$\hat{e_{n}}=\frac{\nabla\phi}{|\nabla\phi|}$$However the answer is given using metric tensor which I am not able to derive. Here is the answer...

Hi. Which is the easiest way to calculate the standard deviation (error) of the magnetic susceptibility by a Monte Carlo simulation? Thanks!

I have been teaching undergrad students informally, and one of the math problems that I have always enjoyed introducing them to is how to compute the area under a gaussian curve, or to keep it simple, the area under the curve ##z=e^{-x^2}## One of my students asked me a question that has...

I am working on a synthesizer project and have reached a point that I am stumped on. I am in this part trying to work from a basic curve of y=1/x^c (where x≥1): As I understand, area under the curve between x=1 and x=100,000,000 (ie. more than I need for a rough approximation) would be...

Homework Statement Question attached in attachments Homework Equations Area enclosed by polar graph is ∫0.5r^2 where r is the radius as a function of angle theta The Attempt at a Solution I attempted to use the formula above and I subtracted the area of the inside from the outside but it...

I was hoping this c++ file could be adapted to use as data compression or encryption #include <iostream> #include <cmath> using namespace std; double asil(double t) { cout<<"asil\n"; cout<< cos(t) << endl; double two = 2.0; cout<< sin(sqrt(two)*t) << endl; return sin(sqrt(two)*t); } int...

Hello! (Wave) Using Green's theorem, I want to compute the integral $$\oint_C ydx+xdy$$ where $C$ has the parametric representation $r(t)=2 \cos^3 t i+ 2 \sin^3 t j, (0 \leq t \leq 2 \pi)$. Using Green's theorem, we get that $\oint_C ydx+xdy=\iint_U (1-1)dxdy=0$. I am wondering if we could...

Hi all, I performed a resonance experiment over the past two weeks, in which I collected the intensity of a Fabry-Perot cavity whilst adjusting the mirror distance with a piezo-element (the specific setup of the experiment is fairly detached from the question I will ask). My raw data is...

Hey guys, I've got this problem I can't seem to get past. I need to find the tangent line to a parametric curve at t=\frac{\pi}{4} I thought I solved the equation, but my answer doesn't seem to be registered as correct. I'm guessing that means I stuffed up the equation, but I can't see where...