Natural Definition and 1000 Threads

Homework Statement Find the area under the given equation using definite integration. y = 4ln(3-x) from 0 to 2 The Attempt at a Solution Integration from 0 to 2 4 (integration from 0 to 2) (3-x) Let u = 3-x du = -dx -du = dx -4(integration from 0 to 2) du Idk where to go from there :/...

if a free-free bar has a crack located somewhere along it's length, in order to find the natural frequency of the bar do you split the bar on either side of the crack and assume each bar is free/excited? What would the equation for natural frequency be in this situation?

Hey there I need to find the natural frequency of a Cantilever Beam. The beam is tapered in breadth, but has a uniform thickness. So basically the end goal is an equation for f as a function of the angle of the side cut. Clamped at one end L=constant B=changes though the length of the...

EDIT: finite dimensional only! Hello, I would like to ask a question; I understand that the cannonical "evaluation map" ( (p(v))(f) = f(v) , f is a functional, v in V ) from V -> V** is a "natural" isomorphism ( we don't have to select any bases, the isomorphism relies on no choices ), so V...

Homework Statement Model the above beam with 3 elements(image provided in attachment). Calculate and list the first 6 natural frequencies Plot the mode shapes corresponding to each of the natural frequencies Homework Equations DET(M^{-1}*K + [I] \omega^2)=0 shape functions...

\ Is \ \mathbb{N} \ dense \ in \ itself.

Well I've been doing fairly complex thermodynamics in classical mechanics lectures with a bit of medium to advanced class, first of all , it took me a very long time to wrap my head around the concept of Entropy, however I still don't understand why we use ln (Natural Log) to calculate the...

Show there exist a natural number n... 1. Let {xn} be a sequence of reals which converges to x > 0. Show that there is a natural number n0 such that xn > 0 for all n >= n0 . I tried this but cannot approach the answer. Can anybody?

I am just learning about the theory of Evolution and wonder how parallel evolution of unrelated species during the same period of time is explained.

Hi I want to derive a natural frequency equation for a system. I saw this question in a book. so they gave us an equation frequency = (1/2pi) * ( sqrt( k/m1+m2+m3/3+4m4+Ic/r2) ) Ic = Moment of inertia of pulley about rotational axis r = effective radius of pulley k = spring constant now the...

So I know that every smooth manifold can be endowed with a Riemannian structure. In particular though, I'm wondering if there is a natural structure for the unitary and special unitary groups. I often see people using the "trace/Hilbert-Schmidt" inner product on these spaces, where \langle X...

Hi everyone, So, resonance, are resonant frequencies and natural frequencies the same thing with a different name? If not could someone please explain the difference. Been searching for the answer for over an hour. Thanks in advance Peter

Homework Statement The methane in natural gas burns completely in oxygen according to the reaction equation: CH4 +__O2 → __CO2 + __H2O Homework Equations a) Complete the reaction equation by filling in the missing coefficients for oxygen, carbon dioxide and water. b) How many kilograms...

I'm not entirely sure that this question doesn't belong in the Earth sciences forum, so my apologies if I've goofed. I'm trying to figure out what academic path to take in order to best be qualified to do field research out in the natural world as often as possible, and secondarily in as...

If I am correct, crystal frequencies depend on the size, shape/cut, and purity of a crystal(?) How can you measure (what instrumentation) the frequency/ies of a natural crystal (other than just quartz)?

hi... we see this phenomenon in our everyday lilfe...:redface: in a sink, if we open its hole suddenly, the water gushes toward it in circular manner and not directly... why the water has to first circle the hole and then it passes through the hole...why it never takes the shortest...

Homework Statement what is the integral of ln(e2x-1) dx 2. The attempt at a solution I got u= ln(e2x-1) du = 2e2x-1 \ e2x-1 du = 2 dx 1/2(integral of u du) 1/2 ln (e2x-1 ) +c = 1/4 [ln (e2x-1 )]2 + c Could you please let me know if this is correct? I don't know how to integrate ln...

How can i find a bijection from N( natural numbers) to Q[X] ( polynomials with coefficient in rational numbers ). I can't find a solution for this. Can you please point me in the right direction ?

Homework Statement Given the Equation ln(x+1)-ln(x)=0 find x (If it exists. Homework Equations The Attempt at a Solution ln(x+1)-ln(x)=0 ln(x+1)=ln(x) x+1 = x 1 = x-x Solution does not exist. (My book "agrees" with me in the solutions.) However, typing up the...

Homework Statement (1) Real variables x and y are related by the equation 3ln(y +4) = 2ln(x +2) − 2ln(x +9)+3ln(x^2 − 1). Determine the range of values of x and y for which the expressions on each side of this equation are defined. Find y explicitly as a function of x, that is...

Homework Statement Evaluate. Integral of (x^5 + 1) / (x^6 + 6x) on x from 2 to 3. \int_2^3 (x^5 + 1) / (x^6 +6x) dx Homework Equations Not sure! The book only seems to give an equation for integrals in the form of du/u, which is integral 1/u*du = ln |u| + C. It also says...

May I ask how to find the E\left(ln x\right) and Var\left(ln x)? The X_{i} are random sample from the f\left(x; \theta\right) = \theta x^{\theta - 1}I_{\left(0, 1\right)}\left(x\right) where \theta > 0. I need the information in finally solving the Cramer-Rao lower bound for the variance of...

I'm calculating the natural frequency of a piping system that is spanning between two points, the formula is the square route of various terms, including the effective axial force in the piping. This is taken from a design code, see below: f = C * SQRT[(E.I/M.L^4)(1+Seff/Pcr+C.(d/D)^2] C =...

How can I show that: \sum_{i=0}^{n}2^{n-i} {n+i \choose i}=2^{2^{n}} for every natural numbers

How can I solve that type of equation: x^2+y^2=4z^2 or x^2+3y^2=4z^2

Prove that sum 1/2^(n+1)*n/(n+1), from n=0 to infinity, converges to 1 - log(2), where log stands for the natural logarithm. I know that the Taylor series for log(x) about x=1 is sum (-1)^(n+1)*(x-1)^n/n, but I don't see how these two statements are consistent. Thanks for any pointers!

Homework Statement Find v(t) across a cap. in a series rlc circuit with no driving force (initial v across cap: 24V) Homework Equations from the values of the components, \alpha > \omega_0, the circuit is overdamped, and the following equation can be used: v(t) =A_1 e^{s_1 t} + A_2...

What is natural line width of laser? how one can determine it e.g. for semiconductor lasers?

Hi, I need to estimate the sloshing natural frequency, in the three axis of a rectuangular tank, not fully filled of liquid. I need this for understading how changes the vehicle dynamics in some trucks. I have found a linear formula for the horizontal direction, but I have found nothing...

As I understand evolution, with natural selection, nature kills the weakest, for an example predators killing the slowest in a herd of Antilopes. What I don't understand is how life could have evolved into something as complex as us in only 2.5 billion years. I've heard of epigenetics, but that...

how do we find the natural frequency of a tower of a wind turbine if, say, the tower is circular hollow cross sectional shape (its not tapered or anything, just cylindrical all the way up). I think i know how to find it when we're ignoring its weight, but what is it when weretaking into account...

How can i solve that equation: x^2 + y^2 = z^2-1 or x^2 + 3y^2 = z^2?

Do we have at present any knowledge whether our natural constants (gravity constant, Planck's constant, ...) are rational or irrational numbers? Thanks, Trinitiet

Homework Statement A certain spring elongates 9mm when it is suspended vertically and a block of mass M is hung on it. The natural frequency of this mass-spring system is: a)0.014 b) 5.3Hz c) 31.8Hz d) 181.7 e) need to know M x=9mm mass=M Homework Equations I don't know any...

Homework Statement Hi. I'm trying to work out the undamped natural frequency of a cantilever beam. The setup of the system is shown in the image below. http://www.flickr.com/photos/56901717@N03/5249378659/ Data:(all lengths measured from the hinge on the left of the beam) Beam...

I've been asked to express the inverse hyperbolic secant function arcsech in terms of the natural logarithm and am unsure as to where to begin in solving such a problem? could someone please point me in the right direction?

Homework Statement My homework problem is the double integral of y/1+xy dxdy. It is a definite double integral and both integrands have the values of a = 0 and b = 1. Homework Equations Integration by parts: uv - int(vdu) The Attempt at a Solution My first step of the double integral is I...

Hello, I am taking a vibrations course and we are currently talking about using PDEs to find responses of beams. In the book, there is an equation to find the natural frequencies of a simply supported beam under an axial load: omega = (pi^2/l^2)*sqrt(EI/roA)*sqrt(n^4 + (n^2*P*l^2)/(pi^2*EI))...

Homework Statement Solve the compound interest formula for t by using natural logarithms. Homework Equations A=P(1+\frac{r}{n})^{nt} The Attempt at a Solution I start by dividing both sides by P. I then take the natural log of both sides and end up with ln(\frac{A}{P})=nt *...

ok i need some clarification if you have a circuit where a current source is in parallel with an inductor a resistor and a capacitor is this considered a natural response or a step response. I guess i thought a step response is if a switch is switched and a source is added then it is a step...

Hi everyone, I'm a beginer in communication science. I have very fundamental question. We know that natural radio waves are emmited from sun to Earth (as a part of their electromagnetic spectrum); what will happpen if our communication devices uses radio waves of same frequency and wavelength...

Homework Statement Use Natural Logarithms to solve for x in terms of y y = \frac{e^{10x}+e^{-10x}}{e^{10x}-e^{-10x}} Homework Equations I am not too sure. The Attempt at a Solution I multiplied both sides by the denominator first. Then I multiply by an LCD of e^{10x} I end up...

I think there are only two primary languages, i.e. natural language and mathematical one, which we use to communicate . If we go one step further, then I would say even mathematics is a subset of natural language where we use symbols and other signs to represent our concepts, ideas into...

Homework Statement Given G =U −TS+PV −BaM show that S(T,Ba,P) = -(dG/dT)Ba,P Homework Equations The Attempt at a Solution I know how to proceed if there are two variables and attemped to use this giving dG = dU - TdS - SdT +PdV +VdP - BadM -MdBa Using central...

How do I start to evaluate this integral? \int\frac{1}{\ln x}-\frac{1}{(\ln x)^2} dx I tried subbing u=\ln x but I'm getting no where... The answer is [tex]\frac{x}{\ln x}+C[/itex] If I differentiate the answer, I get the integral easily, but the reverse... I'm having trouble figuring out...

I am doing a small physics research project introducing sound, resonance, and natural resonance frequencies, but I have questions. I know that resonance is the tendency of a system to oscillate with larger amplitudes at some frequencies rather than others. Does this just mean that the...

Today I went along my uncle to get the natural gas cylinder refilled. He uses it at his farm. When the refilling man placed it on the weighing scale it weighed, let's say, 7 kg. During the refilling process the cylinder was placed on the scale. Once he removed the refilling pipe after the...

Homework Statement I have a linear elastic spring with spring constant E, The spring is mass less, and is held fixed at the left terminal and has a mass m attached on the right terminal. We can neglict gravitational forces. Find the natural oscillation when the tension sigma = E*epsilon...

we all know the mass are attract to another mass so i want know if there are studies and assays to understand really what are the mass

Alright, admittedly I'm a noob at LQG, but I have a basic question. The cosmological natural selection, as I understand it, is that universes are born from singularities (or something close) inside of black holes and 'bounce', inflate, and become universes like our own. But what spawned this...