Analytical Definition and 260 Threads

Is it possible to solve the next transcendental equation analytically (obviously for k): sinh(k)=(b/2)(1+(e^(-2kl))) making the assumption that (bl >>1). I think that is not possible, but in an article that i found, they solve it by making that assumption, and they reach to the solution...

About the Analytical Physics constraint writing... I have added a photo about my problem. My problem is why did we write while calculating constraint values as d/2. you will see on the picture what I am saying, I cannot see the reason of writing d/2

I'm working on this differential equation this few days... Could you give some guidance on approximate solutions to it? i(t) is the only function while all others are parameters. \frac{di(t)}{dt} = -\lambda(\sigma\phi\sqrt{i(t)(1-i(t))} + N\mu i(t)(1-i(t)) Thank you a lot!

Hello, Has anyone used Analytical Mechanics by Hand,Finch for their study in Classical Mechanics? Did the authors publish the solution for the questions given in the book? I can't seem to find them any where. Pardon me if i post this question in the wrong section. thanks, yinx

I am trying to solve the following heat equation ODE: d^2T/dr^2+1/r*dT/dr=0 (steady state) or dT/dt=d^2T/dr^2+1/r*dT/dr (transient state) The problem is simple: a ring with r1<r<r2, T(r1)=T1, T(r2)=T2. I have searched the analytical solution for this kind of ODEs in polar coordinate...

Hi, I am trying to do a vibration analysis of a cantilever beam in contact with Earth (in ABAQUS). Now I need to match these results with the analytiocal solution. Could any of you guide me any paper or book where this klind of a problem is solved. So basically I am looking for the...

Guys, I was wondering if any of you has encountered a problem with multiple energy sources and the analytical solution for that problem. Is there any way to formulate this problem "without" superposition? Thanks, Frank

Analytical mechanics "for dummies"? I'm starting my 2nd year course in analytical mechanics tomorrow and am quite worried that I'll get thrown off very early on, as I didn't fully grasp all of the concepts in lagrangian mechanics in my previous mechanics course (only studied up to lagrangian...

Hey all, I have an engineering background with a pretty terrible grounding in statistics and just about all maths that I can't immediately visualize as some kind of dynamic system, so forgive me if this is an obvious question! I am working through a set of derivations for a conditional...

Hello, I am trying to do some self-studying in Byron & Fuller mathematical methods for classical and quantum physics. I have slightly ran aground on this one task of finding 3d Fourier transforms and I can't find the info in the book itself to free me. Google has neither been very fruitfull...

We will be doing a course based entirely on Engineering Mechanics Vol. 2: Dynamics by Meriam and Kraige in the semester coming up. I want to supplement it with some good theoretical grounding in Lagrangian and Hamiltonian mechanics. Now, I cannot handle an entire separate course for those topics...

How important is Analytical Mechanics in Mechanical Engineering? I'm asking that because my regular course does not offer Analytical Mechanics in its original curriculum, so I would have to get it as an elective from Physics course (curriculums are pretty much pre-defined in here). Thing is...

Hello everyone. I'm studying to become a laboratory analyst and I've recently began my studies in microbiology. My studies began with chemistry and now that the focus in my studies has shifted to microbiology for a bit, I see a sudden drop in required accuracy in results of our analysis. I'm...

Nonlinear 1st order ODE \frac{dH}{dt}=B-A*(H-Z)^{3/2} where: B,A and Z are known values H=f(t); H is function of t I've already solve this ODE numerically using a 4th order RK routine. But my question is, it is possible to get an analytical solution for H(t)?

I just got back my score on the writing section of the general GRE. Apparently I got a 3.5, which puts me in the 25th percentile. Now I don't mean to sound arrogant, but writing has always been a strength of mine. When I write papers, either for physics or humanities classes, they usually come...

Homework Statement a block(mass m), is sliding down a long straight ramp with angle theta, this block is undergoing frictional forces(mu) and air resistance proportional to the speed of the block. In its sliding the block reaches a terminal velocity. Determine the equation of motion and...

Hi all, Can anyone show how I'd work out the analytical solution to an infinite series of this form: \sum\limits_{n = 0}^\infty {\exp \left( { - An} \right)} Thanks in advance, F

Analytical definitions vs intuitive (or perhaps "first year") definitions I just began my real analysis course in college and we were given an assignment; a bunch of mathematical terms for us to define. We are asked to define them using two textbooks, one, our first year calculus textbook, the...

Can anyone help me about analytical solution of this Integral? the integral is written in the word file attached here. Many Thanks in advance, Ashkan

Hi all, Anybody pls help me to convert cosmic time to conformal time (numerically)... is there any analytical expression for conformal time, \tau , except d\tau=dt/a(t) ? can we approximate \tau \approx -1/aH ?? pls help... Anuradha

Hello. Someone knows the book: "Analytical Mechanics: An Introduction" by Antonio Fasano, S. Marmi? Is this a good book on mechanics? Thank you.

Hey I am transfering to the University of Florida next semester. Which one of these classes is easier? Business Statistics or Calc 1 w/ analytical geometry? I want to go higher up in Math and I was thinking calc 1 w/ analytical might help me before I take Business Statistics? Right now I am...

Hi, I'm trying to find the analytical solutions to projectile motion, and not just the approximations.I know the Euler approximation for velocity is the inital velocity - acceleration*time, but what is the more accurate analytical solution for velocity.Thank you.

I am trying to derive an equation of motion for a simple electrostatic potential well. Imagine a scenario where an electron (or other charged particle) is released from an arbitrary distance from a fixed (unperturbable) attractive charge (say a proton fixed in space). In 1 dimension, the...

Homework Statement Find analytical expressions for the magnitude and phase of the frequency response for each G(s) below: (a) G(s)\,=\,\frac{20}{s\,\left(s\,+\,5\right)\left(s\,+\,5\right)}(b) G(s)\,=\,\frac{2\,\left(s\,+\,5\right)}{\left(s\,+\,1\right)\,\left(s\,+\,10\right)}(c)...

Like if I wanted to show how sin z, cos z, or e^z are analytical, what is the general process I have to do? Can I use the cauchy - riemann relations somehow? (where z = x + iy is complex)

Homework Statement I had this question on a test. No one I talked to had a clue how to solve it, and our professor will not be publishing solutions. Any insight as to how to approach this would be great because I am totally stumped. Let f \in C^\infty[-1,1] such that for all j \in N...

LaTex Code: \frac{\partial U}{\partial t} + ax\frac{\partial U}{\partial x} + b\frac{\partial^2 U}{\partial x^2} = 0 Can someone please tell me how to solve this PDE? Thanks, Geoff

Homework Statement you want to prepare 500 ml of 1 M KNO3 at 20 C, but your lab and water are 24 C. How many grams of solid KNO3 (density= 2.109 g/ml) should be dissolved in a volume of 500 ml at 24 C so that the concentration will be 1 M at 20 C? what apparent mass of KNO3 weighed in air is...

Homework Statement The Hamiltonian for the one-dimensional harmonic oscillator is given by: H = \frac{p^2}{2m}+ \frac{mw^2q^2}{2} Homework Equations (a) Express H in terms of the following coordinates: a = \sqrt{\frac{mw}{2}} (q+i\frac{p}{mw}) a^* = \sqrt{\frac{mw}{2}} (q-i\frac{p}{mw})...

Hello everybody, I am a newbie in using Matlab and i have faced a problem i haven't been able to overcome so far,so i decided to share it with you. I would like to solve the following equation in Matlab: (-2*t...

hello everyone I am just new here i need help with my homework here's the problem A cross skier skis 7.40 km in the direction 45° east of south then 2.80 km in the direction 30.0° north of east and finally 5.20 km in the direction 22.0° west of north . Find the resultant vector using...

I have the equation del^2 phi =1 for 2-d (x and y) with the boundary condition being 0 along all 4 edges. I've looked in all my math books and can't find how to solve this. If anyone could get me started I would appreciate it.

Hi. The question is attached as well as my attempt at the answer, which I'm pretty sure is at least partially wrong. I have'ne included my calculations at point B as I have uploaded the limit of 3 files but I got BC=18.30kN (compression) Any help would be great thanks.

I'm interested in calculating (followed by optimizing) the uniformity of a magnetic field generated by an array of neodymium magnets. Let us assume we have an array of neodymium bar magnets, -each with a constant depth (10mm) and height (2300mm). -Multiple segments (with alternating poles)...

source: http://www.scientificamerican.com/article.cfm?id=depressions-evolutionary&page=2 Interesting. So ,depression is linked to high analytical thinking skills; They are saying the reason why some people who isolate themselves from external stimuli like social interaction and not eating...

Homework Statement at 20 degree celcius, the solubility of a solid substance x in water is 42g/L. There are 3 solutions containing x kept at this temperature: S1 contains 5.1g/L,S2 contains 39g/L, and S3 contains 57g/L.so, how to make a saturated solution containing 45g x per litre overall for...

at 20 degree celcius, the solubility of a solid substance x in water is 42g/L. There are 3 solutions containing x kept at this temperature: S1 5.1g/L, S2 contains 39g/L, and S3 contains 57g/L. if we want to make S1 saturated with x, is it possible that we can add an equal volume of S2 and S1...

Homework Statement A rigid container,maintained at 50 degree celcius, is evacuated by a vacuum pump. After this, some liquid n-propanol is introduced into the container. part of the liquid will flash off inside the vacuum,but eventually the system will settle into equilibrium. what is the...

Homework Statement http://img23.imageshack.us/img23/8680/68366634.gif 1.2.1 only! Homework Equations The Attempt at a Solution mPR=1/2 tan(1/2)=26.57 mRN= -1/5 ref angle=11.32 R=11.32+26.57 =37.88 is it correct?

Homework Statement http://img15.imageshack.us/img15/3262/30115975.png Homework Equations all analytical methods The Attempt at a Solution I kinda got stuck for determining the co-ordinates of N, need some help.

Hello MechEs (or anybody else who'd care to reply) I'm about to get a small, but fairly sensitive analytical scale recently (down to 0.01 mg) and now I'm trying to figure out a way to dampen ambient vibration from the room and its surroundings (people walking around, HVAC, etc.) I've got a...

I hope somebody will help me with the following problem. Analytical solutions of cubic equations make use of the method of Cardano. Those solutions give roots that are functions of the coefficients of the equations, being functions where cubic roots are involved. Generally speaking cubic roots...

Hey guys, My cousin came over and was talking about his geometry class and it got me to derive 2*Pi*r and Pi*r^2 using polygons of n sides as n goes to infinity. For the area I ended up using a taylor expansion of sin to weasel myself out of a 0 times infinity, but this is not being very...

Homework Statement A ball is fired vertically upward from the top outside ledge of a 256ft high building with an initial velocity of 160ft/sec. Assue lgl=32.0 ft/sec^2. Homework Equations What is the speed of the ball at t=3 seconds? and What is the velocity of the ball just before...

https://www.youtube.com/watch?v=J_o_Ob-9Ees I wonder could this have anything to do with Cheney doing Bush's thinking for him? Bush just forgot what being analytical was?

Is it possible to develop your analytical skills? I have read before that you can increase your analytical ability by solving puzzles(soduku) but I do not know if there is any research that proves that one can actually increase their analytical reasoning. I was actually thinking about buying...

I was thinking about gauss's law and ran into this contradiction. Consider this situation in electrostatics. You have an infinite line of charge, uniform charge density [text]\lambda[/tex]. In cgs units, E at a distance r from the line of charge along the +y axis (assuming a left handed...

I have been assigned a task that I have found to be very difficult - to try and develop an alaytical (mathematical) expression for the output voltage with respect to time of the cockroft-walton voltage doubler shown below (so that I can plot the transient response), when the input voltage is a...

Homework Statement Find the mg of Fe in vitamin pill. Vitamin pill was dissolved in 25mL HCl which was then diluted to 250mL with water in flask. 25mL of that solution was then diluted to 100mL in another flask. 10mL of the second was diluted to 100mL in another flask. Absorbance of the last...