Chain Definition and 939 Threads

Homework Statement Please have a look at the picture attach, which shows the proof of the D'alembert's solution to the wave equation. If you can't open the open, https://www.physicsforums.com/attachment.php?attachmentid=54937&stc=1&d=1358917223 click onto this...

I have a chain of similar pendula which is mounted equidistantly along a horizontal axis with adjacent pendula being connected with light strings. Each pendulum can rotate within the axis but can not move sideways. at the page http://btakashi.jp/archives/935 scroll to the bottom of the page and...

Homework Statement compute the gradient: ln(z / (sqrt(x^2-y^2)) Homework Equations ∇=(∂/(∂x)) + ... for y and z I just want to know how to do the first term with respect to x The Attempt at a Solution I am so rusty I don't know where to begin.

Hi, I'm trying to simulate a discrete time time markov chain in matlab. Unfortunately I am neither a markov chain expert or a good MATLAB coder. My problem is simple, I have a transition probability matrix with 100 states (100x100) and I want to simulate a 1000 steps beginning from state 1...

This guy relates the calculus chain rule to a popular mob movie. You should really check it out. This is one of the newer videos but people like the way this guy explains things. Here is the link: Ghetto Dude Relates Calculus Chain Rule To "THE MOB" - YouTube

Air is being pumped into a spherical balloon at a rate of 5 cm3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm. So, to solve, I know HOW to do it, I just don't know WHY it's right. \frac{dv}{dr}=4pi r^{2}...

Homework Statement Show that: \frac{dx^\nu}{d \lambda} \partial_\nu \frac{dx^\mu}{d \lambda} = \frac{d^2 x^\mu}{d \lambda^2} The Attempt at a Solution Well, I could simply cancel the dx^nu and get the desired result; that I do understand. But what about actually looking at...

Homework Statement f(x,y) = y' = \frac{y+x^2-2}{x+1} , y(0) = 2 Write the formula for the 2nd order Taylor approximation I just want to ask a question Homework Equations Taylor seriesThe Attempt at a Solution Taylor: y(x) = y(x_0) + y'(x_0)(x-x_0) + \frac{y''(x_0)(x-x_0)^2 }{2} = \\...

Homework Statement As part of a problem I am doing I am asked to show uβ∂βuα = aα where u is 4 velocity and a refers to 4 acceleration. The way to do this is not immediately obvious to me, especially since the problem implies there should be a chain rule step involved which I am not seeing. I...

Homework Statement If u=f(x,y) where x=escost and y=essint show that d2u/dx2+d2u/dy2 = e-2s[d2u/ds2+d2u/dt2 Homework Equations http://s11.postimage.org/sjwt1wkvl/Untitled.jpg The Attempt at a Solution ok i don't understand how they got to that i don't know what d/ds is...

Homework Statement Find the derivative of y = sin(πx)2 Homework Equations Chain Rule: y' = f'(u) * u' The Attempt at a Solution (See attached image) The answer according to the textbook is 2π2xcos(πx)2. What am I doing wrong here?

Homework Statement Suppose g(x,y)=f(x-y,y-s) Homework Equations Nothing else The Attempt at a Solution Find dg/dx + dg/dy

Homework Statement Hi guys, I'm absolutely desperate on the following problem: Consider a random walker who can make steps only to neighbor sites in "D" dimensions where D is an arbitrary natural number. Assume that the distance between 2 adjacent sites is the same for all sites and that the...

Homework Statement the question is about a very flexible strain falling on a rigid table and ask for expression of normal reaction of table at a certain instant Homework Equations when i was trying to solve problem , i resolve N(normal reaction) into N1, N2 which N2 is the weight of...

Homework Statement Ok I have this general homogeneous function, which is a C^1 function: f(tx,ty)=t^k f(x,y) And then I have to show that this function satisfies this Euler equation: x\frac{\partial f}{\partial x}(x,y)+y\frac{\partial f}{\partial y}(x,y)=k\cdot f(x,y) Homework...

Homework Statement Find the energy released for the reactions in the Proton-Proton chain. Homework Equations Proton-Proton Chain: 1H + 1H -> 2H + e+ + v e+ + e- -> γ + γ 2H + 1H -> 3He + γ 3He + 3He -> 4He + 2 1H The Attempt at a Solution To find the energy released in each...

Hi all, I've got a Calculus III Question Homework Statement Find the derivative zs and zt, where z=sin(x)cos(2y)Homework Equations x=s+t y=s-t The Attempt at a Solution I had a go at the solution and this was what I ended up getting for zs, I ended up getting (cosxcos2y)(1)-2sinxsin2y(1)...

Okay so, I am having trouble figuring out what exactly to do in implicit differentiation and usage of the chain rule. Like, I keep getting the wrong answer somehow. See, from what I understand you have to find the derivative of both sides then use the chain rule or something and then solve for...

Homework Statement I'm curious to know if I'm actually doing this correctly. Suppose f(x,y) is a function where x = p(s,t) and y = g(s,t) so that w(s,t) = f(x,y). Compute ws and then wst Homework Equations Chain Rule. The Attempt at a Solution So! Let's compute ws first. Whenever I use a...

Let g(t) = f(tx, ty). Using the chain rule, we get g'(t) = (\frac{\partial f}{\partial x})(tx, ty) * x + (\frac{\partial f}{\partial y})(tx, ty) * y this was actually part of a proof and what i don't understand is that why didn't they write (\frac{\partial f}{\partial (tx)}) and...

Evaluate partial derivative. chain rule?? I would like to represent the term identified in the image as (term 1) in terms of those partial derviatives that are known. Unfortunatly I just can't seem to wrap my head around it at the moment. :bugeye: A prod in the right direction would be...

A chain consisting of five links, each of mass 0.145 kg, is lifted vertically with a constant acceleration of a = 2.6 m/s2. Consider the force link 3 exerts on link 2. (Chains are numbered 5 to 1 going down) Find the magnitude of this force. F=ma I don't know what to consider...

Homework Statement Given that f(x,y) = g(r,\theta), where x = r\cos\theta and y = r\sin\theta, find formulae for \frac{∂f}{∂x} and \frac{∂f}{∂y} expressed entirely in terms of r, \theta, \frac{∂g}{∂r} , \frac{∂g}{∂\theta} . The Attempt at a Solution I said \frac{∂f}{∂x} =...

$x = r\cos\theta$ and $y=r\sin\theta$ $$ \frac{\partial u}{\partial\theta} = \frac{\partial u}{\partial x}\frac{\partial x}{\partial\theta} + \frac{\partial u}{\partial y}\frac{\partial y}{\partial\theta} = -r\sin\theta\frac{\partial u}{\partial x} + r\cos\theta\frac{\partial u}{\partial y} $$...

I am trying to find out how much force is being transferred into a drive chain. Here's the info as I was given: Motor: 150HP RPM: 1750 Gearbox information: ratio: 39:44 Input HP 223 Output shaft to sprocket 6" dia. Sprocket 20" dia. Top of tooth to bottom of root 1-3/8" 4" pitch of chain No...

Homework Statement A uniform flexible chain of length L ,with weight per unit length λ , passes over a small frictionless peg..It is released from a rest position with a length of chain x hanging from one side and a length L-x from the other side .Find the accelaration a as a function of x...

Hi, Is it possible to install two main drives in one chain conveyor to boost up the chain conveyor speed? If possible how to synchronize between the two main drive motors. The motors will control by inverter. Thanks!

Homework Statement Parametrize the upper half of the unit circle by x = cos(t), y = sin(t), for 0\leq t \leq\pi Let T = f(x,y) be the temperature at the point (x,y) on the upper half of the circle. Suppose that: \frac{\partial T}{\partial x} = 4x - 2y \frac{\partial T}{\partial y} = -2x +...

say you have a function f(x,y) \nablaf= \partialf/\partialx + \partialf/\partialy however when y is a function of x the situation is more complicated first off \partialf/\partialx = \partialf/\partialx +(\partialf/\partialy) (\partialy/\partialx) ( i wrote partial of y to x in case y was...

ok stupid question probably- take v(velocity) to be a function of x and x to be a function of t(time). then dv/dt=vdv/dx that's cool but in the hint in problem 2.12 classical mechanics by john r taylor he equates vdv/dx and 1/2(dv^2)/dx that is- vdv/dx=1/2(dv^2)/dx Could someone please...

Hi Homework Statement A chain rotates fast. Observation: the chain gets into a horizontal position. Why? Homework Equations L=I \omega E= \frac 1 2 I \omega² E=\frac 1 2 \frac {L²} I The Attempt at a Solution Well, I have two equations for the energy. I know that I...

Homework Statement A heavy chain with a mass per unit length ρ is pulled by the constant force F along a horizontal surface consisting of a smooth section and a rough section.The chain is initially at rest on the rough surface with x=0 .If the coefficient of kinetic friction between the...

Hi folks, I don't know if my experience is at all common (and I would like some feedback on this if possible), but I can't seem to nail down the properties of euler's number in the context of chain rule problems. Here is the nub of my difficulty: 1. $\text{If }f(x)=e^x \text{then }f'(x)=e^x$...

I have attached a pdf setting forth my question. This is a write up of a lesson i just had on yourtutor, in which i think the tutor might have made an error: this is a direct quote from the whiteboard: $Let g(x)=2x, f(y)=e^y\Rightarrow(fog)(x)=f(g(x))=f(2x)=e^{2x}$$\\Now...

A uniform chain of mass M and length L is held in vertically in such a way that its lower end just touches the floor. The chain is released from rest in this position. Any portion that strikes the floor comes to rest. Assuming that the chain does not form a heap on the floor, calculate the force...

Hi, I have been doing research in my spare time this summer on calculus proofs. I am working on a mathematics degree and I am working to understand calculus inside and out. It has been going really well but I have sort of hit a bump with the calc 1 chain rule. Here is my attempt: lim h -> 0...

Can someone help me out with what I believe who.d be a straight chain rule application? D/dx (dy/dx)^2 I would think, applying the chain rule, you get 2 (dy/dx) d/dx (dy/dx) = 2 (dy/dx) (d2y/dx2) But, from the papers I checked, the (dy/dx) in the answer goes away, leaving just 2...

Hi all, I am trying to understand the concept of Markov Chain (a scan copy of 2 pages is attached), before this text I already studied the notes on Markov Chains at: http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter11.pdf I am lil' confused at the...

If h(x) = ax, g(x) = bx and f(x) = g(h(x)). Wouldn't h'(x) = a? And g'(x) = b? And f'(x) = ab? But the chain rule says f'(x) must equal h'(x)g'(h(x)), so that means f'(x) = ab(ax) = (a^2)bx. Am I missing something obvious?

I have read a few sources regarding the chain rule, and a pervasive explanation that most of the sources share is this, which is way to sort of make sense of it: "Regard du/dx as the rate of change of u with respect to x, dy/du as the rate of change of y with respect to u, and dy/dx as the...

Homework Statement A uniform chain with a mass of M and a length of L is put on a horizantal table in a way that half of it is hanging from the air. At the moment t=0 the chain is released from rest. 1. What is the speed of the chain as its tip will leave the table? 2. Answer question 1...

1. Find the derivative of the function 2. \left(y= x sin\sqrt{x}\right) 3. I started using the product rule and then proceeded to use the chain rule, but I am wondering if I should have used the chain rule twice rather than starting with the product rule. Since I know that x is the...

I know that Young's modulus for a spring is Y= K*L/A where K: is the stiffness of the spring L: the original length of the spring A: the cross sectional area How does this formula change in the case of continuously distributed springs over a ring chain of radius R and a...

proton beta plus decay --proton proton chain Im a biologist so forgive the ignorance. In beta-plus decay, a proton decays into a neutron and emmits a β+ and an electron neutrino. If the neutron is more massive than the proton where did the extra mass come from? Im asking in the context...

I was reading over a textbook that stated the following, where y(s,t) = v(x(s,t),t) \frac{\partial y}{\partial t} = \frac{\partial v}{\partial x}\frac{\partial x}{\partial t} + \frac{\partial v}{\partial t} and \frac{\partial^2y}{\partial t^2} = \frac{\partial^2 v}{\partial x^2}\left (...

I am using a Markov Chain to get the 10 best search results from the union of 3 different search engines. The top 10 results are taken from each engine to form a set of 30 results. The chain starts at State x, a uniform distribution of set S = {1,2,3,...30}. If the current state is page i...

Homework Statement A mass of 200 kg is hanging directly in the center of a chain; the chain makes a 20o angle from its horizontal. The chain will break if more than 2000 N of force are applied at any point on the chain. Will the chain break?Homework Equations F=ma Tfy=mg(sin\Theta) g=10m/s The...

The title says it all. It looks like the configuration probability only depends on where you want to go, not what state you are in now. Yet when I watch simulations, there is clearly a dependence on the previous state. Is there something pretty basic I'm misunderstanding about configuration...

Homework Statement [SIZE="5"](x^{2}-x^{-1}+1)(x^{3}+2x-6)^{7} Homework Equations Chain Rule & Power RuleThe Attempt at a Solution [SIZE="5"](x^{3}+2x-6)^{6}[(x^{3}+2x-6)(2x+x^{-2})+7(3x^{2}+2)(x^{2}-x^{-1}+1)] This is the farthest I've gotten but when I do additional computation I do not...

Homework Statement s=\sqrt{(3x^2)+(6y^2)} Homework Equations None The Attempt at a Solution \stackrel{ds}{dt}=\stackrel{d}{dt}\sqrt{(3x^2)+(6y^2)} \stackrel{3x}{\sqrt{(3x^2)+(6y^2)}} The problem with that is its only d/dx if y is a set number. I don't know how to...