Curve Definition and 1000 Threads

When waves are propagated through medium, the displacement curve will move up and down. Do they have any relationship with propagated energy? For example, when energy is gained from other part the curve will rise up or fall down. And does energy in standing waves share similar principle?

1. Imagine two columns between which is hung a string. The hung string may be expressed graphically and mathematically as a parabola whose nature is exponential. If these columns are moved closer together or farther apart, the hung string becomes more loose or taut according to a trigonometric...

i'm looking for a curve that would have a shape of a snowdrop (the white spring flower) in 3D space. i have tried some sine and cosine functions but they don't give me the right shape. if anyone knows how solve this problem feel free to comment :) (i have tried f(x,y)= sin (x*x + y*y)/(x*x +...

Homework Statement . Let ##C## be a curve that doesn't pass through the origin and let ##P## be the closest point on the curve to the origin. Prove that the tangent to ##C## at ##P## is orthogonal to the vector ##P##. The attempt at a solution. Suppose ##P=\gamma(t_0)##, I want to...

Hi everyone, I'm currently looking for a book on ways to sketch curves, especially for the more unusual kinds of curves, something that teaches things like hyperbolic curves, x^x, sigmoid functions and so on. These are what I have not encountered in my learning very often, so I'm interested to...

In mathematics, what is the name (type) for a curve given by velocity and time dilation? Specifically, I want to find a name for the curve y=1/(1-x^2)^{1/2} This curve is derived from the equation of a unit circle (x-a)^2+(y-b)^2=r^2 where y=(1-x^2)^{1/2}

I'm trying to work out the equation of a curve through 5 very specific points... these points are (47.5, 46.3) (45,48.1) (43, 38.1) (40, 32.8) (37, 26.5) Thought of having general equation ax^4+bx^3+cx^2+dx+e and subbing all the points in and solving but that would take way too long... If...

Is there a software(preferably free) that can fit data into a 4 parameter equation? like the generalised logistic function

Hi All, I have searched for hours but cannot figure this out. I need to find the equation for an exponential curve but I only have the x and y values. Is there a way to do this without using excel? I tried to follow this on YouTube: https://www.youtube.com/watch?v=ta4MZS7w2VA but the equation...

Hello! :-) I' have a problem... I fitted experimental data with a second order exponential theoretical curve: y = A1*exp(-x/t1)+ A2*exp(-x/t2) + y0 and I have these data for 4 repetitions of the same experiment: first time: Reduced Chi-Sqr = 6,81066E-4 Adj. R-Square = 0,41005...

$r=5$ and $\theta=\pi/6$$\frac{dy}{dx}=\frac{\frac{dy}{d \theta}}{\frac{dx}{d \theta}}=\frac{\frac{dr}{d \theta}sin(\theta)+rcos(\theta)}{\frac{dr}{d \theta}cos(\theta)-rsin(\theta)}$ $\frac{0*sin(\pi/3)+5cos(\pi/3)}{0*cos(\pi/3)-5sin(\pi/3)}=-\frac{\sqrt{3}}{3}$is that right?

find the area of the region that lies inside the first curve and outside the second curve. $r=3cos(\theta)$, $r=1+cos(\theta)$ $3cos(\theta)=1+cos(\theta)$ $2cos(\theta)=1$ $cos(\theta)=\frac{1}{2}$ $\theta= \frac{\pi}{3}, \frac{5 \pi}{3}$$A=\frac{1}{2} \int_{\pi/3}^{5\pi/3} \ (3cos(\theta))^2...

find the exact area of the surface obtained by rotating the given curve about the x-axis. $x=cos^3(\theta)$, $y=sin^3(\theta)$, $0 \le \theta \le \pi/2$. $\frac{dx}{d \theta}=-3sin(\theta)cos^2(\theta)$ $\frac{dy}{d \theta}= 3sin^2 (\theta)cos( \theta)$ $S=2 \pi \int_{0}^{\pi/2} \...

find an equation of the tangent to the curve at the point corresponding to the given value of the parameter $x=t\cos\left({t}\right)$, $y=t\sin\left({t}\right)$, $t=-\pi$ help me

(sorry in advance for not knowing how to use laTex and also not knowing calculus, I thought maybe before I teach myself calculus to figure out this one problem maybe you all could fill in what I'm not figuring out... Thanks in advance...) I recently found out that I needed to know calculus in...

Does anyone know of an online calculator that can form an equation of a curve with complex values and lots parameters? An advanced curve fitting calculator Y= C1(1/(1+C2e^C3x) for example

Homework Statement I think that the image is clear. There isn't friction, not the material point with wedge, not the wedge with the floor. At time t=0 the material point start to move, I need to find the final speed of the two objects at time t\rightarrow\infty. Homework Equations...

Hello guys, I was watching video about physical basis for arrow of time.. ..as well as several other videos and articles about physics of time. I am puzzled with this picture here (seen in 35:07 in video above)...

this is actually for computer programming. I'm trying to show a line which plots the course taken by a ship. It's in space so drag etc are not an issue but it can continue to accelerate. I felt initally the answer was to take the end point and figure out the angle between the current...

I have been reading about rotation curves, and the I understand the basics, but I am trying to understand the basis / meaning of the curves? Are the findings based on redshifts of individual stars / "bins of light" at set distances from the centre of the galaxy? And given that the...

1. Hi, I have been asked to calculate the area beneath a curve. The curve is y = 2x^2 + 7x + 24 and the values of x to find the area within are 5 and 2. 3. My attempt stands as follows: A = 5,2∫ (2x^2+7x+24)dx [ 2x^3/2 + 7x^2/2 + 24x...

Could someone send me some examples of B-spline curve and NURBS curve? Thank you

http://www.askamathematician.com/2011/04/q-why-is-the-integralantiderivative-the-area-under-a-function/ this website says f^\prime (c) (B-A) = f(B)-f(A) or f(c) (B-A) = F(B)-F(A) (since F’ =f). but seems like this is wrong. because B-A= Δ x, f'(c)*Δ x= Δy and the area might...

Homework Statement Calculate the arclength of the curve given parametrically by ## x=2t^2, y=\frac 8 5 \sqrt 3t^ \frac 5 2, z=2t^3 ## for 0≤t≤2 Homework Equations ## S=∫ \sqrt(dx^2 + dy^2 + dz^2) ## The Attempt at a Solution 1. Found derivative of each and input into equation. ##...

What is f(x) when eg x = 0, 1, 2, 3, 4, 5, 6, etc y = 0, 8, 12, 14, 15, 15.5, 15.75 etc (the y value at x =1 is arbitrary) ie each successive y value adds half the difference of the preceding 2 values. (It is effectively the inverse of a first order exponential decay where the y...

guys I need loads of help for this question(s)? what do i even do ?!? Sketch the curve y = lnx and find the tangent line to this curve at the point where the curve crosses the x-axis. Deduce that, for small delta, ln(1 + δ) ≈ δ . - I know what the y = Inx curve looks like but what do i do...

Homework Statement What is the x-intercept of the line tangent to the curve x(t) = 3 + cos(∏t), y(t) = t^2 + t + 1, when t = 1? Homework Equations Derivative, y=mx+b The Attempt at a Solution To find the line tangent to the curve: d/dt = <-∏sin(∏t), 2t+1> at t=1 <-∏, 3> dy/dx = dy/du *...

Hi I just wondering how to report negative values cuased by non-zero intersection. For example, when the absorbance<0.037 in the figure, the concentration would be negative. Thank you!

Homework Statement Find the length of the curve r = cos(θ) - sin(θ), 0<θ<∏/4 Homework Equations L=∫ds ds=sqrt(r^2 + (dr/dθ)^2) The Attempt at a Solution r^2 = (cosθ - sinθ)^2 = cos^2(θ) -2cosθsinθ + sin^2(θ) =1-2cosθsinθ dr/dθ = -sinθ -cosθ (dr/dθ)^2 = 1+2cosθsinθ...

Hi, I always wondered, what is the area under an inexisting curve. That arctan(1/sqroot(x^2-1)) for example. Its domain does not include from -1 to 1. If I take its integral from 0 to 10, what answer should I get?

Suppose I have a smooth curve \gamma:[0,1] \to M, where M is a smooth m-dimensional manifold such that \gamma(0) = \gamma(1), and \hat{\gamma}:=\gamma|_{[0,1)} is an injection. Suppose further that \gamma is an immersion; i.e., the pushforward \gamma_* is injective at every t\in [0,1]. Claim...

Homework Statement Find the length of the curve r=cosΘ - sinΘ, 0≤Θ≤∏/4 Homework Equations Arc length = ∫|v| dt The Attempt at a Solution I found r'(θ), then used the arc length formula. Arc length = ∫ sqrt (sin^2 Θ + cos^2 Θ) = ∫ dΘ and integrated it to find ∫dΘ = ∏/4 The correct answer...

Homework Statement Let the curve C be given by ##\vec{r}(t)=3t^{2}\hat{\imath}-\sqrt{t}\hat{\jmath}## between ##0 \leq t \leq 4##. Calculate ##\int_{C} xy^{2}dx+(x+y)dy##. Homework Equations The Attempt at a Solution First find the derivative of r...

Given a curve ##\gamma: I \to M## where ##I\subset \mathbb{R}## and ##M## is a manifold, the tangent vector to the curve at ##\gamma(0) = p \in M## is defined in some modern differential geomtery texts to be the differential operator $$V_{\gamma(0)}= \gamma_* \left(\frac{d}{dt}\right)_{t=0}.$$...

Homework Statement Determine where r(t) is a smooth curve for -pi <t<pi R(t)= (x(t),y(t))=(4sin^3(t), 4cos^3(t)) Homework Equations The Attempt at a Solution To be honest I have no idea where to start. I know what a smooth function is but my understanding is that the sin(t) and...

Homework Statement can anyone give me hint on how to show the tangent will not meet the curve again? Homework Equations The Attempt at a Solution

I'm doing research and I have some data (attached -- 'y' = first column, 'x' = second column in CSV format) that I need to find a general curve fit for (function = f(x)/x). This will help me do future predictions. Here are my stipulations: The fit curve must have the format of f(x)/x. Two...

Is there any real life phenomenon that can be modeled by the curve: S(t) = 1/(1+e^-t) ? in the range between t=-5 and t=5 Thanks!

Homework Statement A mass ##m## on the end of a light spring of force constant ##k## stretches the spring to a length ##l## when at rest. The mass is now set into motion so it executes up and down vibrations while swinging back and forth as a pendulum. The mass moves in a figure-eight pattern...

Here's an example of the graphs I am currently studying. http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/imgnuk/bcurv.gif I think I have a fundamental misunderstanding of its meaning that I would love to get past. I understand that Fe-56 is the most stable nucleus (although I'm not sure...

Homework Statement The graph of the polar curve r=2-cosΘ for 0≤θ≤2pi is shown in the figure. (attached) a) write an integral expression for the area of the region inside the curve b) write expressions for dx/dΘ and dy/dΘ in terms of Θ c) find dy/dx as a function of Θ d) write an equation in...

how can we understand torsion of curve is in the direction of normal unit vector en?

Here is the question: I have posted a link there to this thread so the OP can view my work.

Find the equation of the curve that passes through the point$$ (1,2)$$ and has a slope of $\displaystyle\left( 3+\frac{1}{x}\right)$ at any point $$(x,y)$$ on the curve. $(A) 2xe^{3x-3}$ $(B) 2xe^{3x+3}$ $(C) 2xe^3$ $(D) 2e^{3x-3}$ $$A(1)=2$$ and $$D(1)=2 $$ so $$B$$ and $$C$$ are out...

I have several data points with error bars, and these error bars are different sizes for each of the data points. I'd like to fit a model function to them which has non-linear parameters, and be able to get error bars on the model parameters, ie. if my model is something like f(x) = A +...

Homework Statement For u(x1, x2) = ax1 + bx2 a) find total differential b) Draw a representative level curve for u = ubar (u with a line over it) c) Find MRS (marginal rate of substitution) Homework Equations u(x1, x2) = ax1 + bx2 The Attempt at a Solution a) fx1 = a fx2...

Hey all, I am trying to find a function which will give me a family of curves similar to the one shown below. What I am hoping is that a single parameter will control whether the curve starts out slow (like the blue one) or whether the curve starts out fast (like the green one) or whether it...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement complete problem attached Homework Equations The Attempt at a Solution part I in this question was a bit tricky but i managed to solve it , when i read part II i understood nothing , he usually asks about the tangent not the normal , he asks about the point...

Hello, Are spectral reflectance curves dependent on the interface between the reflector and surrounding medium? For example would they be different if I had a silver mirror in air compared with silver mirror in a semiconductor? I think they would be because of the refractive index contrast...