Curve Definition and 1000 Threads

Why is the solution to the brachistochrone problem a curve at all? If the idea is to get from a higher point to a lower point under the influence of gravity alone, why is a straight line not quicker than a cycloid? It seems counter-intuitive that the shortest time would be along a curve and not...

I have generated the graph shown below and now would like to describe it at a high-level according to the curved nature of the plotted line. Besides simply stating observations such as the exponential growth at approximately x = 0.19, is there a classification or term for the shape of the curve...

This is my first thread on the forum. I'm really glad to have found this wonderful resource. I have a lot of intuition in mathematics and one of my dreams has been to have the same level of intuition in physics. With your help I hope I can achieve that. I was reading an example in Physics...

What first thing I should do to solve the function of a basic open b-spline curve where the coordinate of its control points are such as written below? x1,y1 = 0,0 x2,y2 = 1,3 x3,y3 = 3,5 x4,y4 = 5,6 x5,y5 = 7,5 x6,y6 = 9,3 x7,y7 = 10,0

Hi: In mechanics of materials. I learned that the deflection of a beam can be characterized by its elastic curve which is the deformed neutral axis. But I am bothered by the fact that, if two end of a beam is fixed, and the elastic curve is continuous in between, then it must mean...

Homework Statement A curve is traced by a point P(x,y) which moves such that its distance from the point A(-1,1) is three times its distance from the point B(2,-1). Determine the equation of the curve. Homework Equations None The Attempt at a Solution Distance from Point A to...

Hello folks, If we have the expression, say \frac{∂f}{∂r}+\frac{∂f}{∂θ}, am I allowed to change it to \frac{df}{dr}+\frac{df}{dr}\frac{dr}{dθ}, if "f" is constrained to the curve r=r(θ). My reasoning is that since the curve equation is known, then f does not really depend on the...

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

Hello, I am doing simulation using Finite element for the concrete ,this I found the concrete model for the concrete in euro code as attached in the picture. But what I don't understand is basically why the peak of the curve is not the Fck (compressive strength), because the curve maximum is...

How to test if a metric contain close timelike curve? I read somewhere that if the space coordinate change from positive to negative then it contain close timelike curve. For example, a metric gmn=-Adt2+Bdr2+Cdθ2+Ddz2, if C is negative, then it contain close timelike curve. Is that correct...

How would a galaxy rotation curve look if every matter simply had a 6 times larger mass than the visible? (please neglect how that could be) Wouldn't a same size galaxy then reside in a 6 times larger gravitational well so that the spiral arms would still be in the steep part of the well...

find the length of a curve given by: f(x)=integral(upper bound: x lower bound: 0) (cos^2(x)+4cos(x)+1)^0.5 dx Here's my solution: I use the equation L=integral ( upper bound: a lower bound: b ) sqrt[1+(f'(x))^2] f'(x)=(cos^2(x)+4cos(x)+1)^0.5 1+[f'(x)]^2=2+cos^(x)+4cos(x)=[cos(x)+2]^2-2...

My understanding is that the presence of energy and matter curve spacetime. Is a photon considered energy? If so, how can it curve spacetime while having zero rest mass?

Hi, I've attached the problem and the solution. I understand the solution except for one thing. I've circled the part I'm having problems with. How do I decide if the circled part should be f2(x,y,z)=x2-y2-z or f2(x,y,z)=z-x2+y2 I'm sure it has something to do with the fact that the problem...

Homework Statement Find the area under the curve of the function y=5x^2+3 from x=0 to x=2 Homework Equations - The Attempt at a Solution First I sketched it out on paper, finding that at x=2,y=28. I created a rectangle with l*w of 6 (3*2), would the remaining area not included...

I was wondering about the spectral radiancy curve of a black body. How does the spectral radiancy of any other body looks like. I have seen one among many possibilities: http://www.giss.nasa.gov/research/briefs/schmidt_05/ Q 1. But i was thinking that for a general body (not a black body)...

Homework Statement The question is attached! Homework Equations mgsintheta = downward force on incline The Attempt at a Solution I was thinking that this has something to do with the downward force on the incline and making sure that the car doesn't slide down the incline. Changing...

Studying for precal exam.. for some reason I can't figure this out no matter how I try it Homework Statement Find the area under the curve for y=x^2 going from x=0 to x=2 Homework Equations - The Attempt at a Solution I first graphed the equation and sketched it on paper. I...

Hi I have always wonder about this. I understand the concept of bevel gear, but never quite see how the involute profile would function in a bevel gear. assuming that there is a tooth(either of the driving or driven gear) located at the center between two gears ( where it has the...

Hi, I need some directions to target a problem that is bothering me quite a lot, even some links or small explanation if possible, thank you in advance! I have a huge dataset Ω (unknown) of experimental values {e_i} that should approximate (with noise both in the value and in the...

Homework Statement Find the equation of the tangent line at the curve y= x * e^(2x) at the point (2, 2*e^(4)) Homework Equations The Attempt at a Solution f'(x)= e^(2x) * (2x+ 1) (e^4)(5) = 5e^4 y- 2*e^4 = 5*e^4 (x-2) y= 5(e^4)*x - 8*(e^4) Is this right? It seems too easy...

HiI have always wonder about this. I understand the concept of bevel gear, but never quite see how the involute profile would function in a bevel gear. assuming that there is a tooth(either of the driving or driven gear) located at the center between two gears ( where it has the greatest...

Hi everyone, I've been racking my brain about this problem, but can't seem to figure it out. It seems like it should be easy, but I keep getting confused. Let's say I have an arbitrary parametric curve r(t)=<x(t), y(t)>. I want the velocity in the tangential direction to be constant. That...

Hi I had a quick question. From what I understand resonance is when a natural frequency of an object is matched by the driver frequency however in this graph it seems as though resonance is occurring at all the frequencies around the natural frequency just not to a great extent...

Homework Statement Hi guys, I just wanted to confirm I am doing this right. I have a graph of energy (Joules) vs. time (seconds). I need to get the force from this information. If I know the linear distance the object has traveled, can I use the work equation W= Force* Distance, and solve...

I was looking to the definition of the Bell curve, and the Gaussian distribution, but I don't see any difference when we represent them in a graph. Both have the same Bell curve. What is the difference between the Bell curve and the Gaussian distribution?

I'm taking a first year physics course and have been having a little trouble with the basics of Newtons laws and forces and whatnot, though nothing that can't be fixed with a bit more hard work. I'm looking ahead now and seeing a lot of EM material, and after kind of taking a brief look at...

I'm taking a first year physics course and have been having a little trouble with the basics of Newtons laws and forces and whatnot, though nothing that can't be fixed with a bit more hard work. I'm looking ahead now and seeing a lot of EM material, and after kind of taking a brief look at...

From pressure-volume curve of the lung and chest wall (attached photo), I don't understand why would the elastic recoil pressure of the lung is initially negative then becomes positive above 30% of vital capacity when the lung volume increases from residual volume? What I initially thought...

Here is the question: Here is a link to the question: How do you solve this really hard calculus question? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement r(t)=(t^2+t)i+(t^3-4)j+(3-t)k r(t) hits the xy plane at the point (12,23,0). Find the angle on intersection of r(t) with the xy plane at that point. Angle= Homework Equations cosθ=(AxB)/lAllBl The Attempt at a Solution I find the answer was 0.0017 degree...

Hello, I'm in need of someone to show me how to fit a bacterial growth curve to data in Prism, preferably using the Gompertz function. I also need someone to show me how to assess the goodness of this fit. I have many different growth curves and I need to compare the parameters. Hopefully...

Problem statement, I am calculating the time it takes for my motorcycle to reach 55 miles per hour, through its engine Horsepower, Torque, transmission gearing, and sprocket gearing.(chain driven) I am using the equations: F=[mass/g]*[dV/dt] dt=[mass/g]*[dV/F] t=∫[mass/g]*[dV/F]...

Homework Statement Given that the curve y = x^3 has a tangent line that passes through point (0, 2), find the area of the region enclosed by the curve and the line by the following steps. Homework Equations The Attempt at a Solution Let f(x) = x^3 and let the coordinates of the...

Homework Statement Excuse my terminology, not sure what the actual translations are. Find a simple (no holes in it), closed, positively oriented, continuously differentiable curve T in the plane such that: \int_{T}(4y^3+y^2x-4y)dx + (8x +x^2y-x^3)dy is as big as possible, finally...

If I was given some n(very large) points, and if I want to fit a curve circularly, I think I should go for least squares method. What is the optimal way to do it? can someone explain me clearly how to proceed using least squares method? I don't how to proceed. But I know I should do least...

Homework Statement Evaluate: A: \int^{16}_0 (\sqrt{x} - 1)\,dx B: \int^4_1 \frac{2}{\sqrt{x}}\,dx C: \int^6_2 \frac{4}{x^3}\,dx Homework Equations n/a The Attempt at a Solution Its part C which I think I have done wrong, but the others could be too. Part A: \int^{16}_0 (\sqrt{x} -...

Homework Statement Identify the symmetries of the curve. Homework Equations r = 8 + 7sinθ The Attempt at a Solution x-axis: (r,-θ) ---> 8 + 7sin(-θ) = 8-sinθ (not equal to ) 8+7sinθ; not symmetric about x-axis. y-axis: (-r,-θ) ---> -8+7sinθ (not equal to) 8+7sinθ; not symmetric...

Homework Statement Curve C is given in Polar Coordinates by the equation r=2+3sinθ. Consider the usual Cartesian plane and take O as the pole and the positive x-axis as the polar axis. Find points on the curve C where the tangent lines are horizontal or vertical and sketch the curve C...

Homework Statement Consider the parametric curve given by the equation x(t) = ti + t^(1/3)j1. Calculate x'(t). Does the vector exist at t=0? 2. Find a new parametrisation of the curve for which the tangent vector is well defined at all points. What is the value of the vector at the origin?The...

Hi, my lecturer has given us two graphs showing the general shapes of the max torque curves for both gasoline and diesel engines, and they clearly show that the diesel engine has a much flatter torque curve than the gasoline engine, but not explained why. Expected to find this information...

I'm trying to figure out how to do a Lissajous Curve in 3d. It has a 2d shape in the real world, so if it's in the real world, then there must be a 3d shape to it. Here is the crazy version, it has 8 variants of the last pic layered and it's at 45 45 0 This is the one above and it is at...

Homework Statement I have two questions. 1) generally speaking, when we are given two equations both describing surface in R3: f1(x,y,z)=k and f2(x,y,z)=C, The intersection of the two will be a curve that's by solving both equations. My question is, by solving f1 and f2 to get anther...

Homework Statement If f(x,y) = xy, find the gradient vector \nabla f(3,2) and use it to find the tangent line to the level curve f(x,y) = 6 at the point (3,2) Homework Equations The Attempt at a Solution f(x,y)=xy \Rightarrow\nabla f(x,y)=<y,x>,\nabla f(3,2)=<2,3> \nabla...

Note: If this is the wrong sub-forum for this question please move it. I was not sure if this question should go in the General section or not. Question: I want to create a smooth non-piecewise curve in ℝ^{3} (3-space) such that it's intersection with the xy-plane consists of the integer...

Homework Statement Explain in terms of stress and strain what happens to the stretched material beyond the ultimate tensile stress. Homework Equations A curve similar to this The Attempt at a Solution I can see that the curve beyond UTS represents increasing stiffness but i can't...

Hello MHB, Find and an equation of the tangent(s) to the curve at the given point $$x=2\sin(2t)$$, $$y=2\sin(t)$$ $$\left(\sqrt{3},1 \right)$$ first we need to find the slope so we derivate $$\frac{dy}{dt}=2\cos(t)$$, $$\frac{dx}{dt}=4\cos(2t)$$ so we got $$\frac{dy}{dx}=...

Homework Statement Find dy/dx on the curve 1/3*y^3 + y*sin(x) = 1 - x^6 At which points on the curve does this derivative does not exist? Find the slope of the line tangent to the curve at the point (0,3^(1/3)). Homework Equations dy/dx = - Fx/Fy The Attempt at a Solution I solved dy/dx...

Hey all, I'm in the process of writing a report concerning the physics of rollercoasters going around banked curves. With the rollercoaster I'm focussing on, the velocity of the car is always greater than the designed velocity of curves meaning there is a friction force parallel to the bank...

hello good morning. Let look at the two diagram. (back view) In STATIC, a car is remauning static at a bank curve and its force diagram is as follows. for this case, the normal force is smaller than the weight of the car and friction exists in the directiin perpendicular to car. In MOTION...