Natural Definition and 1000 Threads

  1. T

    Question about Natural Frequency and Resonance

    So, I was reading a book on Nikola Tesla the other day, and it said that he said that he could theoretically split the Earth in two with resonance. If I had a variable frequency oscillator, and I knew the natural frequency of an object, obviously I could create a standing wave. But, could I, as...
  2. D

    Natural gas, Water, standard oil. say motor oil properties

    https://www.physicsforums.com/attachments/42263 https://www.physicsforums.com/attachments/42264 how we doing? i was just wondering does anyone have the properties of the following similar to the images attached.Natural gas, Water, standard oil. say motor oil properties.any oil properties...
  3. L

    How can you find the natural frequency of an aircraft?

    Hi How can you find the natural frequency of an aircraft? It would be of great help if anybody can give me an idea of how to go about the problem.
  4. G

    Natural State of Matter Rest or Motion?

    Hi, I'm studying Roman culture and civilizations in a course at my university and I'm learning how poets and philosophers argued that the natural state of matter is in motion, that everything is always in motion and never at rest, that there is an empty void that exists between objects and...
  5. I

    First year calculus proving two formulas are equivalent with natural logs

    Homework Statement Show that the two formulas are equivalent integral [sec x dx] = ln|sec x + tan x| + C integral [sec x dx] = -ln|sec x - tan x| + C Homework Equations Pythagorean ID's? Log rule of addition The Attempt at a Solution Well, I realized the formulas can only be equivalent if...
  6. R

    Showing that Increasing sequences of natural numbers is uncountable

    Homework Statement Show that A, the set of all increasing sequences of natural numbers is uncountable Homework Equations I know that the natural numbers themselves are countable. The Attempt at a Solution I am thinking of using some sort of diagonal argument to prove this.
  7. C

    How Does the Natural Exponential Function Influence Trigonometric Outcomes?

    1. Let f(x)=sin(e^x) a. Find 2 values of x satisfying f(x)=0 b. What is the range of f(x) c. Find the value(s) of x that maximize f on [3.8,4] (use calculus) 2. y=e^x if and only if x=ln y 3.a. x=-infinity because the limit of e^x as x approaches -infinity is 0. and also...
  8. D

    Trying to make a program to take and print the natural log of a number input

    I'm relatively new to C programming and I am trying to make a program to take and print the natural log of a number input by the user but for some reason my program always returns incorrect answers. For example I entered 1 as my number, and the answer came back as some ridiculously big value...
  9. J

    Beautiful Natural Oceanic Diffraction Patterns

    Hi, I was having a flick around Google maps whilst procrastinating and came across this when I looked at some islands off the Australian coast. I'm not 100% certain that the pattern is caused by diffraction of the waves passing through the gap between Bernier and Dorre Islands, or simply...
  10. C

    Particle Distance/Velocity - Natural Logarithms

    Homework Statement I'm going to post an image due to the complex syntax in the problem... The Attempt at a Solution I'm not going to lie... I really have no idea where to even begin with this problem. Because it says total distance traveled by the particle, I'm assuming that the...
  11. S

    Given any real numbers a and b such that a<b, prove that for any natural number n

    Given any real numbers a and b such that a < b, prove that for any natural number n, there are real numbers x1, x2, x3, ... , xn such that a < x1 < x2 < x3 < ... < xn < b. The hint I was given says : Define xi recursively by x1 = (a+b)/2 and x(i+1) = (xi +b)/2. Prove that xi < xi + 1 < b...
  12. S

    Can damping affect the prediction of resonance using natural frequency?

    Can I say that the natural frequency is the frequency of a system vibrating without effect of forces and including all parameters of damping that could occur on the system? Resonance would occur when the forcing frequency equals the antural frequency.
  13. M

    Understanding Rotation Axis in Equilibrium: Exploring Torque and Center of Mass

    This is about a little thing that I have a lot of trouble understanding, and which always bugs me when studying equilibrium. I've often tried to apply the concepts of torque in this context, but nothing ever seems to make sense. I consider a uniform rod which is initially at rest, and is not...
  14. S

    Log-Likelihood ratio in the context of natural language processing

    First of all, let me apologize if this question is in the wrong place. It's fundamentally a statistics question but it relates to computer science. I'm also not sure if this falls under the "homework" category, since it's for a class, but I need assistance on a general idea, not a problem set...
  15. U

    Understanding Vibrations: Natural Modes and Frequencies

    Hi, I'm trying to understand vibrations and specifically what happens in the natural modes of frequency.. 1. It seems that the harmonic nature of solution(with Acos(wt)...where A is the amplitude) applies only in the natural mode of vibration...and so the system will have a defined mode...
  16. C

    Property of Natural Log- Inequality equation

    Hi. I just saw on wikipedia that natural logarithm has such a property: [x/(1+x)] < ln (1 + x) < x (http://en.wikipedia.org/wiki/Natural_logarithm) Can anyone pls tell me how to prove this? Proving [x/(1+x)] and ln (1 + x) less than 'x' is easy.. But how abt [x/(1+x)] < ln (1 + x)...
  17. V

    Calculate natural line width of the transition

    Homework Statement A lifetime of the first excited state for some atom is τ, calculate natural line width for that line. The Attempt at a Solution Well, I could use energy-time uncertainty relation ΔE*Δt=h then ΔE*τ=h , now I can use a relation E=hc/λ to obitain Δλ=c*τ , which is...
  18. W

    Natural parametrization of pdfs

    I am struggling to understand the concept of natural parametrization of pdf of exponential family. Say that we have a function with the following pdf: f(x;\theta)=exp\left[\sum_{j=1}^k A_j(\theta)B_j(x)+C(x)+D(\theta)\right] where A and D are functions of \theta alone and B and C are functions...
  19. A

    Need help understanding proof of natural log integrals

    [PLAIN]http://img31.imageshack.us/img31/9004/screenshot20111117at720.png Proofs always get to me for some reason. It's like other problems I can do, but when it comes to proofs I don't know what to put. Can anyone show me steps? Thank you
  20. M

    Help with mathematical assertions for natural numbers

    Homework Statement Prove by Mathematical Induction that the assertion, n ∑ r^2 = n/6 (n+1)(2n+1) r=1 holds for every natural number n. Homework Equations Ok, so basically, how do you solve this question? I have got to the Induction step but I'm not sure how to do it...
  21. R

    Natural vs. Synthetic rubber foam ? search project solution help

    Hello everybody I have a mass production project for a new product . The thing is to be made in foam , sheets...it is some material involved . To visualize the idea think about the Yoga mat sort of material but much thick.. Natural or Synthetic ?..provided there is to be found a natural...
  22. H

    Existence of a natural number X

    Homework Statement Given M \in N, show that there exists an X \in N such that for all n \geq X , n^2+n+1 \succ M Homework Equations The Attempt at a Solution Since both M and X are natural numbers and I am just trying to prove the existence of a certain natural number X, I...
  23. J

    When are you supposed to take the natural log of both sides of an equation?

    It seems this is done randomly, yet it must not be random, there must be some logic to it, but when do you know to do it? What is like a clue or the rules that indicate you can/should take the natural log of both sides of an equation?
  24. H

    Finding the natural frequency of a steel beam

    Homework Statement I am trying to calculate the natural frequency of a steel beam. Homework Equations I=1/12*W*T^3 Volume= T*W*L M0=V*ρ K=(3EI/L^3) Meff=(33/140)*M0+Mend ωn=√(k/Meff) The Attempt at a Solution This should be a simple plug and chug problem but I can't see what...
  25. S

    Finding the Solution for x in a Natural Logarithm Equation

    Homework Statement Solve for x xln(x)-24+6ln(x)-4x=0 My attempt at the solution I first moved "-24" and "-4x" to the right side of the equation yielding xln(x)+6ln(x)=24+4x I then converted the natural logarithms to exponent form and product form yielding ln(x)^x+ln(x)^6...
  26. I

    Proof: Applications of the Universal Property of Natural Numbers

    Homework Statement N refers to the set of all natural numbers. Part 2: From the previous problem, we have σn : N → N for all n ε N. Show that for any n ε N, σ(n+1)(N) is a subset of σn(N), where we have used n + 1 for σ(n) as we defined in class. 2. The attempt at a solution For Part 2, I...
  27. Matt Benesi

    Question about formula for natural log

    Any information on the following formula for natural logarithm (I looked in wikipedia and Mathworld but didn't see it). It came from another equation I was working on a bit ago, and I was curious about it as I didn't recall seeing it before (which doesn't mean I haven't), although it reminded...
  28. M

    Double integral of a Log (natural)

    Homework Statement I wish to find the following integral over the rectangle [-a,a] in u and [-b,b] in v using Mathematica. The constants a and b are positive (and non-zero). The variables x and y are in Reals. A(x,y)=\int_{-a}^a{\int_{-b}^b{\log{\left[(u-x)^2+(v-y)^2\right]}{\rm d}v}{\rm...
  29. D

    Natural frequency of large degree of freedom system

    I have a spring-mass system with 200 masses and 199 springs. All masses are 100 tonnes and stiffness 20 MN. The boundary conditions are fixed-free. I have constructed a lumped mass matrix and stiffness matrix and calculated the lowest natural frequency. Including the boundary conditions I...
  30. H

    Exploring the Relationship Between Natural Log and Partial Derivatives in PDE

    Is the following relationship true?: \frac{\partial (ln(k))}{\partial P}=\frac{1}{k}\frac{\partial k}{\partial P} I am getting both of these terms from a paper on mineral physics and they seem to use both terms interchangeably. If so, how are these related?
  31. S

    Natural Frequency and mode shapes

    Hi I am using Ansys to find the natural frequency of a structure but this has meant that my understanding of vibrations has become unstuck. When I last studied natural frequencies, it was under free vibration. I formed the impression that one structure can have only one natural frequency...
  32. C

    Powerseries of a natural logarithm

    Homework Statement Show that \frac{1}{x} \ln \frac{x+1}{x-1} = \sum_0^\infty \frac{2x^{2n}}{2n+1}. 2. The attempt at a solution I tried to use the relation \frac{1}{1+x} = \frac{d}{dx}\ln (1+x) and expand as a geometric series, but this did not lead anywhere since I then ended...
  33. C

    The Meaning of Natural Units: $c=1$

    What is the meaning of a frame of reference where $c=1$ ? Are these the so called natural units?? And which is the purpose of this??
  34. S

    Is There a Trick to Rewrite This Equation in Terms of t?

    Hi I want to rewrite the following equation in terms of t: X=\exp(-At)-\exp(-Bt) Where X,A and B are positive numbers. The problem is, I have a -exp() term... so I can't take the natural log of this... ie. as far as I am aware the following is not allowed: \ln(-\exp(-Bt)) So...
  35. J

    Derivatives of the Natural Exponential and logarithmic Functions

    1. Hello there, I have a few questions on the derivative homework that I did but not sure if it's right or not. These are difficult and my teacher doesn't go over all of them so I don't know if it is right or not. Please help me so I can understand the concepts before the upcoming test. 1...
  36. 1

    Prove that the product of any three consecutive natural numbers

    Homework Statement Prove that the product of any three consecutive natural numbers is divisible by 6. Homework Equations The Attempt at a Solution wat
  37. T

    Differential Equation Involving Natural Log.

    Homework Statement Calculate the following: \int^{-4}_{-6} (x^-1+5x)dx Homework Equations The Attempt at a Solution I've worked this down to ln(-4) + 5(-4) - ln(-6) - 5(-6) =ln(-4)-ln(-6)+10 The answer to the left half (the ln parts) of the equation is undefined, and the...
  38. M

    State and prove a natural generalization

    Homework Statement State and prove a natural generalization of "prove that for any three positive real numbers x1, x2, x3, x1/x2 + x2/x3 + x3/x1 \geq 3. Homework Equations AG Inequality is used in subproof (x1/x2 + x2/x3 + x3/x1 \geq 3) The Attempt at a Solution I don't know what...
  39. J

    Question about integral and natural log

    Homework Statement Find the integral to the following expression \int\frac{1}{x-1}dx Homework Equations \int udv = uv - \int vdu \int\frac{1}{x}dx = ln(x) The Attempt at a Solution Given the information above, would a correct answer to this problem be ln(x-1) ? If not...
  40. A

    How Do You Differentiate f(x) = (71+x)/(1-x)?

    Homework Statement Differentiate, f(x)=71+x/1-x Homework Equations The Attempt at a Solution Working this out, hoping it's right as I was going along, my final answer is 71+x/1-x * (2ln7)/1-x
  41. K

    What actually is natural frequency?

    when we talk about the phenomenon of resonance, we use the term 'natural frequency'. What actually is natural frequency of an object?...what is meant by matching of natural and applied frequency and why does it produce vibration with maximum amplitude?
  42. T

    Solve for x: Natural Log Help!

    natural log helpp! Homework Statement ln(x+10)+ln(x+4)=2 2. The attempt at a solution okay so i took it down to (-14+-(14^2 - 4(e^2 - 40))^1/2) / 2 which i broke down to 356 - 4e^2 inside the sqrt. am i on the right track and if so Whats the next step?
  43. M

    The Natural Dispersion of Black Holes

    Black holes are believed to be scattered throughout the universe. These ultra-dense bodies have a gravity field so dense that nothing, not even light can escape. If these bodies are able to consume everything that enters its event horizon than over the billions of years that the universe has...
  44. I

    Natural log of a variable times the variable

    so I've got this equation down to x*ln(2/x) = 5 Can someone show/point me to a page where I can see how to solve this. I am under the impression it requires some type of ratio computation. thanks!
  45. M

    Natural Frequency of a Spring System

    A mass m is confined to move in a channel in the x-direction and is connected to four identical springs with spring constant k, which are oriented at angles \phi = 45° as shown, if the system is in static equilibrium. a) Ignoring friction, determine the natural frequency of vibration of the...
  46. S

    Time period and natural frequency

    A fundamnetal question here; IS it that the terminologies natural time period and frequency are used only for simple harmonic motions and not for motions which are periodic/sinusoidal like an SHM?
  47. S

    How do we formalize the following:For all natural Nos :

    How do we formalize the following: For all natural Nos : n^2 is even\Rightarrow n is even
  48. F

    Fibonacci primes equinumerous with the set of Natural numbers?

    I believe that Fibonacci primes are infinite. Currently there is no proof that there is an infinite number of Fibonacci primes. I was wondering why we couldn't compare the set of Fibonacci primes to the set of Natural Numbers and demonstrate that both have cardinality aleph null? Indeed, why...
  49. I_am_learning

    Whose light do you find more natural, Florescent or Incandescent?

    Color Rendering Index is said to measure the extend to which lights behave as natural light .It is said that Incandescent have CRI of 100 and Florescent have around 60-70. However, I find the lights from Incandescent yellow-reddish and I find that objects are rendered yellowish on its light. I...
  50. C

    Wormwood Forest: A Natural History of Chernoby

    Hello everyone. I am the author of "Wormwood Forest: A Natural History of Chernobyl" and stumbled upon your very interesting forum when googling Genn Saji, a Japanese nuclear scientist who has been sending out daily email updates about Fukushima. I am fortunate enough to be on his list and...
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