Natural Definition and 1000 Threads

Homework Statement In the 2p state of lithium, two fine structure components are formed due to spin-orbit interaction. They produce wavelengths of 670.960nm and 670.975nm. Compare Doppler and natural broadening at 700K. The lifetime of the 2p state is 27ns and \frac{\Delta \lambda}{\lambda} ~=...

Homework Statement a) Light of wavelength 510nm is emitted by an electron in an atom behaving as a lightly damped simple harmonic oscillator with a Q value of 3 x 107. Find the natural frequency of the system. b) Find the width of the resonance.Homework Equations The Attempt at a Solution...

Homework Statement What are the natural frequencies (not wavelengths) of oscillation formed in a pipe that is open at both ends and a pipe open at one end and closed at the other? Homework Equations The Attempt at a Solution I don't understand this. I keep reading something about 2L and 4L.

In simple terms (if possible), why is an aircraft unable to achieve the manoeuvrability of a bird, eg, immediate stop, rapid acceleration, sudden change of direction? I'm guessing it relates to necessary strength and rigidity of the plane's structure, engine power/weight ratio.

Homework Statement Find the derivative of y = x^2 + x^(2x)The Attempt at a Solution By looking at the equation I think I need to use implicit differentiation + natural logs. But I can't do anything with: lny = ln(x^2 + x^(2x)) So I assume I'm wrong.. Any help??

I've been told that the natural frequency of an oscillator is the frequency an oscillator will oscillate at when left to itself. Is this referring to the frequency of an ideal oscillator subject to ONLY a restoring force. Because all REAL oscillators are subject to damping and, when left to...

I know the history of how set theory came about and how Cantor showed the real numbers between (0,1) were non-denumerable. He did this by showing that they can't be put into a one-one correspondence with N (1, 2, 3...) ...So what does that really tell me? I know it tells me that the...

Hi everyone. I have learned that: 1+2+3+...=\frac{n(n+1)}{2} 12+22+32=\frac{n(n+1)(2n+1)}{6} I want to know what the general formula of Ʃna, in which n and a are natural numbers, respect to n and a.

If we set c=G=1, then c=1 leads to L=1/T , the G=1 means that M=L^3/T^2 and combining the two means that M=L=1/T so far so good. But say if I also want \hbar=1 this seems to imply M=T/L^2 but combining this with c=1 which gave the L=1/T now suggests that M=1/L=T . Which seems...

Homework Statement Find the force and acceleration of the block down the inclined plane Homework Equations F = ma The Attempt at a Solution We have two unknowns in F = ma I know there is the gravitational force going straight down, and there is the normal force that is...

1. how to integrate∫ (ln x)2 /x dx Homework Equations The Attempt at a Solution

Homework Statement Let y=sin(x)^x. Find dy/dx My teacher said to use Natural long to solve this. she got, step 1:ln(y)=ln(sin(x)^x)=x ln(sin(x)) step 2:y(dy/dx)=1(ln(sin(x)+x(cos(x)/sin(x) Final answer:dy/dx=((sin(x))^x)[ln(sin(x))+x(cos x/sin x) I don't understand how she...

Can someone derive for me the equation ωd=ωnsqrt(1-ζ2) Thanks

how to prove that for any real number in r (0,1) there exist a natural number n in N such that rn > 1

How to prove that it does not exist a natural number having the property that the permutation of the first digit with the last one produces a new number being 5 times bigger compared to the original one Regards

I have array of natural numbers from 1 to n. They are divided into m groups, where m*(m-1)=n. I need all m-1 elements from first group, last m-2 elements from second group, last m-3 elements from third group...zero elements from last group. For example 5*4=20: 1,2,3,4; 5,6,7,8...

Problem: let $\mathbb{N} = \left\{0, ~ 1, ...\right\}$ be the set of natural numbers. Prove that $(\mathbb{N},~\le)$ is a poset under the ordinary order. Solution: let $x \in\mathbb{N}$, then $x \le x$ as of course $x = x$. If also $y \in\mathbb{N}$, then $x \le y$ and $y \le x$ implies $x =...

Homework Statement Evaluate the integrals a) y= b) y= Homework Equations The Attempt at a Solution I've tried using the Reciprocal Rule and substitution of each ln function with u to get a workable result, but haven't come anywhere near a recognizable solution. The answers...

The question is as follows: Using an induction argument if n > 1 is a natural number then n-1 is a natural number. P(n)=n-1 such that n-1 is a natural number Following the steps: Base case: n=2, P(2)=1 which is a natural number. We fix a natural number n and assume that P(n)=n-1 is...

Folks, I am looking at the Ritz method for the following problem ##\displaystyle -\frac{d^2 u}{dx^2}-u+x^2=0## for ##0<x<1## with boundary conditions ##u(0)=0## and ##\displaystyle \frac{du}{dx} |_{x=1} =1## The last derivative term, how do I know whether that is a natural or...

Are there an \aleph_0 # of natural numbers with an \aleph_0 # of digits?

I've actually already completed my first year of college, with quite modest results. Something which has been causing me quite a bit of psychological bother though is whether or not my SAT math score is a reflection of some kind of natural ability or intelligence, rather than a reflection of...

(1) A mass of 3.0 kg is suspended from a vertical spring and produces a static deflection of 60 mm. The system is also subjected to viscous damping of 36 N s/m. Calculate the value of the: (a) natural frequency i. In Hz ii. And rad/s (b) damping ratio...

Many years ago I was sat playing cards with friends when I saw this strange light outside hovering just above a door handle so I went to have a look. It was about the size of a golf ball and had some resemblance to a flame but with very different properties. It was silent. It was in...

Homework Statement I have two problems that I got stuck. 1. \exists ! N\in P(X) , A\Lambda N=A, \forall A\in P(X) and for each A\in P(X), \exists ! A'\in P(X) , A\Lambda A' =N 2. Prove a+(b+c) = (a+b) +c, for positive integers a, b, cHomework Equations 1. Given sets A,B \in P(X), where P(X)...

Homework Statement What does it mean when the derivative of a function f(x) is in the form: d ln f(x) / d ln x ? Is it the logarithmic scale derivative, or something? Homework Equations d ln f(x) / d ln x The Attempt at a Solution Googling.

Hello guys! Is it possible to convert a natural frequency to resonant frequency with maybe some kind of formula? I was given a transfer function and I was asked to draw a root locus plot and determine the resonant frequency. I know how to get the damping ratio and natural frequency and the value...

Dear Physics Forum community, I am posting here as a last resort, so any guidance/references would be much appreciated. As a small part of my project, I need to calculate the natural frequency of metallic solid spheres. All I have been able to find on the web is the Schummann Resonance...

Hello, The definition is ln(x) = \int_1^x\frac{1}{t}dt I have read several sources regarding this, but what I can't seem to find is why it was defined this way. What is the justification for defining it this way, and how was ln (x) found to be the same as the that particular integral?

Hello, The problem is ∫(ln x)/(x + x ln x) dx. I've done most other problems in the set, but don't know where to start with this one. Although we are just learning integration by parts, I'm not sure how this would apply. I can get to ∫u/(1+u) du Thanks for any help. Homework Statement...

Is the set of natural numbers the only infinite set that is not a power set of another set?

I've heard Iron has the most condensed nucleous out of all the elements, and I asume it is due to the enormous amount of pressure in a stars core just before the end of its life. My question is if we made iron in a lab, would its nucleous be just as condensed as natural iron or would it be...

The study of social science phenomena using empirical data such as register data* are very often approached with an regression model. One of the most used approaches is a linear model where the parameters is estimated with ordinary least squares. The models of this type is often called...

Hello all. I have been reading Halmos's Naive set theory. In chapter 12., there is an excercise problem which states I thought a lot about this but this seems like a theorem to me and is not at all trivial to prove it. I would greatly appreciate it if you can give me a hint or a clue as...

Was the evolutionary principle of natural selection at work on the Earth before animate matter(life) emerged? Inanimate chemicals replicated before R/DNA and the first living cell. Did natural selection apply to these chemical molecules? If the answer is yes, is it just a hypothesis or has...

Homework Statement e^2x * e^2 Homework Equations The Attempt at a Solution Really, I'm just a little bit confused on how I would go about adding the exponent. None of the examples in the book cover that. Is it simply e^2x+2?

I wish to show that the sum of 9 consecutive natural numbers: n(n+1)(n+2)(n+3)...(n+8) will not be a perfect square. This problem came by as a result of another problem I was doing and I'm wondering if anyone knows/has come across this already. After some searching I found that n! is not a...

Hi, I had been reading the book on 'Dynamics of Structures' authored by Prof.Anil K Chopra of University of Berkeley. In his book, the author has provided the natural period of vibration of some buildings like: 1) Transamerical building of San Francisco- California which is 2.90 seconds...

How can I convert an equation in units where hbar = c = 1 into an equation with hbar and c in SI units? I searched around a bit and wasn't able to find anything (I'm probably not asking the right question). Is there some general way to do it rather than just intuition from having seen the...

Hello, I'm re-studying calculus using Spivak's Calculus 4ed and I'm stuck in one of the problems. Any help is appreciated. Homework Statement The theorem to prove is "every natural number is either even or odd". The definition of even given by Spivak is the following: A natural number n is...

Is it possible to define an abelian group on the natural numbers (including 0)? It's just that for every binary operation I've tried, I can't find an inverse!

Homework Statement if n is a natural number and n2 is odd, then n is odd Homework Equations odd numbers: 2k+1, where k is an integer even numbers: 2K, where k is an integer The Attempt at a Solution ok so take the opposite to be true, or n2 is odd and n is even. Then we would have...

Natural selection: What do they mean by "average" individual? You know how they say stabilizing selection favors the "average" individual - i.e, it is centered around the mean? I have a question. How do they calculate this "mean"? I'm confused. All I know is that if pure-white rats mate...

If 'n' is a natural number such that n>1, prove that there exists a natural number k such that n-k=1. It raises the question: What is the definition of a natural number? Could you say that because n is natural, n-1 must be natural so that if k = n-1, n-k = 1? BiP

Homework Statement A musicians tuning fork rings at A above middle C, 440Hz. A sound meter level meter indicates the sound intensity decreases by a factor of 5 in 4 seconds. What is Q of the tuning fork? Homework Equations Q=\frac{\omega}{2\beta}...

So a human is made of cells. It is essentially a city or society of cells that live together. There is no such thing as human, it's just a bunch of cells. So human is just a natural phenomenon, an emergent property. In addition, a cell is just a bunch of atoms. I.e. a collection of atoms...

Hi all, A fixed-free bar has a single natural frequency. When we discretize such a bar in the finite element method, then the natural frequencies are the eigenvalues and an nχn matrix where n is the number of the degree of freedom which is usually large. Thus we obtain up to n natural...

I had this posted under the wrong field earlier until I realized it's an applied mathematics question An excerpt from The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner "There is a story about two friends, who were classmates in high school, talking...

An excerpt from The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner "There is a story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a...

I want to prove the next assertion in Jeffrey M. Lee's Manifolds and differential geometry. If \mathcal{D}_1, \mathcal{D}_2 are (natural) graded derivations of degrees r_1,r_2 respectively, then the operator: [\mathcal{D}_1,\mathcal{D}_2] := \mathcal{D}_1 \circ \mathcal{D}_2 - (-1)^{r_1 r_2}...