Analysis Definition and 999 Threads

I'm aware that geometric buckling is equal to material buckling when k =1, any pointers on how to set up the boundary conditions for this problem?

a) λ = 4/3 by considering the energy balance as P moves from A (2a) to B (1/2a). The E.E. at A changes into a gain in gravitational potential energy + build up of E.E. at B since the spring compresses. b) a = 5/3g by considering that the mass P is in dynamic equilibrium immediately after...

Hi, I have a quick question about part 1 of this upper bound theorem question (in the attached image). Answer says that \lambda_c = 2.25 . First, we know that there is 1 redundancy and therefore there will be a maximum of 2 plastic hinges for failure. I have found that there needs to be...

Summary:: Is there somebody can help me？ The book about Mechanics analysis or classical mechanics,if you have read some good books, please recommend them to me, I will be very grateful.

Hello, New to the forum. I am looking for some help with some work. It is dimensional Analysis, i have done Dimensional analysis with the analysis bridge before. But i am stuck with the question below and trying to learn it. Any help much appreciated. I have the equation q = U A dT. But i am...

I have reached a conclusion that no such z can be found. Are there any flaws in my argument? Or are there cases that aren't covered in this? Attempt ##\log(\frac{1}{z})=\ln\frac{1}{|z|}+i\arg(\frac{1}{z})## ##-\log(z)=-\ln|z|-i\arg(z)## For the real part...

ANY AND ALL HELP IS GREATLY APPRECIATED :smile: I have found old posts for this question however after reading through them several times I am having a hard time knowing where to start. I am happy with the sketch that the function is correctly drawn and is neither odd nor even. It's title is...

Should i read Introduction to Calculus and Analysis by Courant? I have calculus background I want to study multivariable and single variable in rigorous way There is a lot of books in this subject like Spivak, apstoal,Courant,... . I am not sure what to choose

Using real science we can extrapolate what hull shapes could be used, assuming we actually did have high thrust constant acceleration drives (we don't because it requires energy/mass ratios that tend to cancel each other out). So what shapes? Pill capsules are ideal for crewed vessels. Even...

I found the Req which is 13.6 and also found the It which is 0.74. I'm having trouble finding the separate current and potential difference numbers.

I’m trying to solve this question using the exact method in my book but I’m having trouble with setting this up. Here is my work** The length of a football field (100 yards) needs to be converted to centimetersLength of paperclip = 3.2 cm long36 inches = 1 yardhow many paperclips in 100 yds =...

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Could I please ask for views on this question: I've answered the whole thing and agree with the answers given in the textbook. Here are those answers (where Y is the modulus of elasticity of the string = lamda in the question): Period of motion = 2 * PI * sqrt( ma/Y ) Speed passing through...

$$r<x<s$$ $$s-r>0$$ We enploy the Archimedean principle where $$n(s-r)>1$$ We employ density of rationals where $$\exists [m,m+1] \in Q$$ Such that $$nr\in [m,m+1)$$ Therefore $$m\leq nr \lt m+1$$$$ \frac m n \leq r \lt \frac m n + \frac 1 n $$ Since $$ \frac m n \leq r $$ Then $$...

Hi, I am a civil engineering student currently taking Statics. We are doing truss analysis in the class right now; and I know that this joint is marked as correct. However, I don't see how this is even possible. I begin by considering this a concurrent 2D force system, Fy = 0 & Fx = 0. The...

Summary: Is Baby Rudin a good choice for first Real Analysis textbook for someone without strong pure math background? I've completed 2 semesters of college calculus, but not "pure math" calculus which is taught to math students. I'm looking for introductory text on Real Analysis and I've...

Hey guys, Got what seems like a simple problem at first, but has been giving me difficulty in trying to prove. Please help me with it and show me what to do because I have no clue really. Here is what it asks: Prove that if A is a countable set and the function f:A\impliesB is onto, then B is...

Summary: Perform nodal analysis on a circuit to find voltages. For a laboratory I am trying to find the nodal voltages for a circuit we built using hand calculations. I have the answer as we ran the simulation which shows all the nodal voltages, however my nodal analysis seems to be wrong as I...

Hi all, I tried to solve this, but I can't find the R(equal). I use the following method. The circuit: For t<0 the switch is closed so the iL(0-)=4 A For t>0 it opens and the iL(∞)=0 A Now, I want to find the value τ=L/R(equal) Then I will use the: iL(t) = iL(∞) + ( iL(0-) - iL(∞) )* (...

In Material Analysis Methods (Material Characterization), how possible to know if the methods are use or popular? I guess that the list published in the following links https://en.wikipedia.org/wiki/List_of_materials_analysis_methods contains the full spectrum of material characterization...

In fusion reactions, lighter nuclei are combined into heavier ones (atomic mass increases); so the direction is from left to right (shown on the diagram). Therefore, in the fusion of 'light elements' the total final binding energy is higher (the related arrow points upward); so ##B_2-B_1>0## and...

I have been reading two books on complex analysis and my problem is that the two books give slightly different and possibly incompatible proofs that, for a function of a complex variable, differentiability implies continuity ... The two books are as follows: "Functions of a Complex Variable...

I recently read this article in Science magazine: "The 200-year effort to see the embryo." by John B. Wallingford. Sadly it is probably not open access. This article reviews the history increasingly detailed information available on developing embryos. Recent technological advances in optical...

I'm asked to solve for Vo for this equation. I've set the bottom node to be my reference node before applying nodal analysis. When included in the KCL equation for node at Vb, will the dependent voltage source 20iΔ be negative since the current through that element is leaving node C? Say, the...

Hello! I am working on a spectroscopy experiment and for each wavelength of a laser I have some counts. For the purpose of my question I will make up some data to illustrate my problem, in the table below (these are just numbers, without any relevance for the physical reality of the experiment)...

Hello there, I am trying to analyze an impeller i found at home (small one) so i can find the torque-speed graph. The thing is that i get stuck in an equation with 3 unknowns instead of 2 and i don't know what else to assume. My approach is as follows: I take the usual equation: ## M = \dot{m} (...

I tried to prove this by absurd stating that there is no such ## \mu'## but i couldn't get anywhere...

Can someone explain it to me exactly how dimensional analysis works (perhaps gives some examples.) What use does it have? Is it a convenient way to check your solutions? My teacher showed this example E ~ G, M, R [E] = k[G^α * M^β *R^γ] Maybe someone can explain this.

Problem Statement: ) A circuit is constructed with six resistors and two ideal batteries as shown. The battery emfs are ε1 = 18 V and ε2 = 12 V. The values for the resistors are: R1 = R5 = 55 Ω, R2 = R6 = 110 Ω, R3 = 44 Ω, and R4 = 117 Ω. The chosen positive directions for the currents are...

It possible a diagram would be really really helpful

For the set A: Note that if n is odd, then ## A = \{ -1 + \frac {2} {n} : \text{n is an odd integer} \} ## . If n is even, A = ## \{1 + ~ \frac {2} {n} : \text{ n is an even integer} \} ## . By a previous exercise, we know that ## \frac {1} {n} ## -> 0. Let ## A_1 ## be the sequence when n...

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I've been going round in circle and am stuggling as maths is not my strong suit. Any ideas? Up to the point where i equate the powers and then confuse myself, any help would be greatly appreciated.

Hi Everyone, I am transferring to Cal in the fall for Engineering Physics and am currently deciding which math track to take. The first option is to enroll in math 121A/121B, which are mathematical methods courses for scientists and engineers (covers series, complex numbers/integration, PDE's...

Good Day, I am trying to pick up small ferro (Neodynium)) magnets vertically with a solenoid. I want to know how much magnetic force the solenoid can pick up. The formula I tested and actual numbers for my solenoid are in the image below. I know that the magnetic field of a solenoid is given...

Here is the question, and my solution is for question (a) : knowns : I = 12 cos 2000t = 12 ∠0° L=0.2 H R=200Ω ω=2000, XL = j*0.2*2000 = j400Ω Zt = (j400*200)/(200+j400) = 178.9 ∠26.57°Ω i want to find the power absorbed by R, so : IR = (Zt /R)*I = (178.9 ∠26.57°Ω/200)*12 ∠0° = 10.73∠26.57°A...

(As a quick note, 'wave flume' should be taken rather generally. I basically just mean the sort of experiments involved in the flow of water which may use instruments such as pressure gauges, load cells, wave gauges, and ADVs. I know that they're not always done in a flume per say -- the...

Unlike in electromagnetics, the nonlinearity of mechanical structures is not only due to the material property. It could be due to large deformation and contact as well. Even though I will be implementing the existing and popular methods, I am still scared and I feel it is not a job that can be...

Does anyone have a recommendation for a book(s) to use for the self-study of real analysis? I have just finished Apostol Calculus, Vol. 2 and would like to move on to real analysis. I am not sure whether I should continue following Apostol and move on to Apostol mathematical analysis or...

I am trying to analyze if the bolts in my design are sufficient to support the load on a shaft. Unfortunately, the bolts are not all located on one face, and though I know how to analyze each face by itself, but I would like to be able to combine them all into one problem. I have attached a...

u=prg LT^-1 = MLT^-2 ML^-3 LT^-2 = (ML^-2T^-2)^a (ML^-3)^b (LT^-2)c L^2 LT^-1 = M^a L^-2a T^-2a M^b L^-3b L^c T^-2c =M^(a+b) L^(-2a+3b+c) T(-2a+2c) M; a+b=0 L;-2a+3b+c=1 + T^-1 Either the formula is mixed up or...

The equation listed is the implicit form. I achieved this a weird way. \begin{array}{|c|c|c|} \hline 1 & 1 & 1*1 \\ \hline 2 & 6 & 2*3 \\ \hline 3 & 18 & 3*6 \\ \hline 4 & 40 & 4*10 \\ \hline 5 & 75 & 5 * 15 \\ \hline 6 & 126 & 6 * 21\\ \end{array} Focusing on the third column now, I can...

That is, for Supernode -1,3 (12V branch) , we do Nodal Analysis and we have (V2-V3)/2 , over the 2 ohm branch. But this current is not included in the Equation 1 in the solution I have attached(Which is my only source to cross check answers/solution right now.) Is the solution wrong? Thanks...

if I am to learn about waves at an undergraduated level, how much is it important to learn Fourier theory before I actually go into the physics?

Problem Statement: so we did an experiment. basically the teacher gave us each a cube of unknown metal and we had to figure out what it was using the specific heat. we put the metal in boiling water until it was 212C and then we put it in room temp water and we measured how much it heated the...

From what I understand is that you can sum up R3 and R4 to get 350 ohms Then you can can a parallel circuit with the missing resistors, 4amp and the new 350 ohm resistor and that's about it. My textbook says the answer is 55 ohms for the resistors and the current is 0.073 but I got 3.75 ohms...

Summary: Looking for guidance on how to model an RLC circuit with a system of ODES, where the variables are the resistor and inductor voltages. This is a maths problem I have to complete for homework. The problem is trying to prove that the attached circuit diagram can be modeled using the...