Ratio Definition and 1000 Threads

Homework Statement The amplitude of an underdamped oscillator decreases to 1/e of its initial value after m complete oscillations. Find an approximate value for the ratio ω/ω0.Homework Equations x''+2βx'+ω02x = 0 where β=b/2m and ω0=√(k/m) x(t) = Ae-βtcos(ω1t-δ) where ω1 has been defined as...

I have designed a test apparatus where I can apply known bending and torsion loads to thin sheets of foamed plastic. All test samples will be identical sized sheets with various treatments to improve stiffness..with the added weight of the treatment recorded. I will use the information to...

With four Rolls-Royce Turbojet engines attached on A380, I wonder, if the optimization of fuel efficiency as its prime design factor/variable? If so, may I know, what it is air by pass ratio?

I have the following summation where a is a positive constant and can be > 1 $$ \sum_{k=2}^{n}a^{n-k} $$ I am trying to find a general formula for this summation, which turns out to be a geometric series with a as the common ratio. I have worked out the following: $$ \sum_{k=2}^{n}a^{n-k} =...

The terminal speed of a sky diver is 188 km/h in the spread-eagle position and 320 km/h in the nosedive position. Assuming that the diver's drag coefficient C does not change from one position to the other, find the ratio of the effective cross-sectional area A in the slower position to that in...

I wasn't sure whether to put this in the mechanical engineering board or not but since electrical engineers typically design electric motors, I'll put it here. From what I hear, all types of electric motors have terrible power-to-weight ratios. So if we were to hypothetically one day have a...

Homework Statement An ideal simple gas turbine has a compression ratio of 5. What is its Homework Equations c=r(γ-1/γ) η=1-(1/c) The Attempt at a Solution I'm stuck, I think I need to use the above equations and possibly more. I just don't know how to find a value for the ratio of...

Homework Statement I desperately need to know something which I consider basic but yet I get different answers all the time for example ratio A:G=1:3 or A:G=1:2 or A:G=1:4 some students are telling me that the ratios should be divided with one another like 1/3=0.33 to get the...

Homework Statement Show that the ratio of the blackbody fluxes from a star at two different frequencies (i.e., a color) is measured, then, in principle, the surface temperature of the star can be derived, even if the star's solid angle on the sky is unknown (e.g., if it is too distant to be...

I take issue with the "Advanced Engineering Electromagnetics" 2nd edition by Balanis again. In Page 156, it claimed for AR=-ve, it is Right Hand rotation, AR=+ve is Left Hand rotation. For plane wave propagates in z direction and at z=0: A)Let Ey lag Ex by \frac{\pi}{2} \Rightarrow\;\vec...

Homework Statement In the vertical jump, an athlete starts from a crouch and jumps upward to reach as high as possible. Even the best athletes spend little more than 1.00 s in the air (their "hang time"). Treat the athlete as a particle and let y_max be his maximum height above the floor...

Hi guys, Revision for an exam tomorrow, I hope someone can help? I've been given the answers but I can't work out how to find the damping ratio without being given a velocity or distance for the mass to travel?A mass of 6kg is suspended on a spring and set oscillating. it is observed that...

Hi all... I'm new here... Homework Statement this is not a homework question, I'm just solving practice questions for exam preparation Two wheels with masses M1 = 2 kg and M2 = 4 kg are connected. The ratio is R1 = 5 cm and R2 = 10 cm Considering an angular velocity of ωo = 10rads-1 for the...

Hi, I am wondering why radial variation in Poisson's ratio exists when a cylinder is compressed? Ie, Poisson's ratio toward the center is lower than what is measured at the circumferential edge. Thanks M

Homework Statement (see attachment for figure) A small object is mounted to the perimeter of a hoop of radius r. The mass of the object and the hoop is same. The hoop is placed into a fixed semi-cylinder shaped rough trough of radius R, such that small mass is at top. Find the least r/R ratio...

Homework Statement Calculate: (3 a + 3 b)/(a - b) If a/b = 2/5 No attempts, I don't know how to solve this. Help?

Homework Statement Part of an elecrial circuit for the olympic score board consisted of a single battery V and several resistors having on of two values. R or 2R. They are hooked up in the confriguration as shown. Calculate the ratio of the two currents shown Ib/Ia...

I am a little bit confused on what an extinction ratio is. I am looking at optical specs and it keeps on coming up. Would someone be kind enough to explain it to me and perhaps provide a mathematical background thank you!

Two spheres S1 and S2 hang from light insulating strings of the same length from points P1 and P2 which are on the same level. S1 is of mass M and has charge Q. S2 is of mass M and has charge 2Q. Repulsion between S1 and S2 causes their strings to be inclined at angles of theta1 and theta2 to...

I was messing around with cellular automata and wanted to test a theory i had. If you look close at the elementary cellular automata Rule 30 you'll notice that the right side is chaotic, while the left side has chaotic properties but it does have order and repetition. There is an imaginary...

Let B=(5,21), C=(40,-14) and $\frac{BP}{PC}$=1/6. What is the most efficent way to find P? My book just states P=(6/7)B+(1/7)C but no idea how they got that.

A=$\begin{bmatrix}1\\1\\0\end{bmatrix}$, B=$\begin{bmatrix}3\\1\\-1\end{bmatrix}$ C=$\begin{bmatrix}5\\3\\-1\end{bmatrix}$, D=$\begin{bmatrix}4\\0\\-2\end{bmatrix}$ Find the coordinates of a point E such that A,B,C,E forms a harmonic range. This means that the cross ratio is -1.

Does anyone have any idea about modulation ratio of voltage and modulation frequency in power systems?What is the relation between between two?

Homework Statement Use the Ratio Test for series to determine whether each of the following series converge or diverge. Make Reasoning Clear. (a) \sum^{∞}_{n=1}\frac{3^{n}}{n^{n}} (b) \sum^{∞}_{n=1}\frac{n!}{n^{\frac{n}{2}}} Homework Equations...

I've been fooling around in MS Excel trying to reconstruct this fractal: I haven't had any issues here making it. I totally understand the algorithm for generating the left turn/right turn ordering. What I really want to know is how this version is generated: Original image...

Homework Statement The binary star system Krell consists of two stars, Krell A and Krell B, orbiting each other, with no other ojects nearby. Assume Krell A, the smaller star of mass mA, moves in a circle of radius rA at speed vA. Krell B, the larger star of mass mB = 2.51mA), moves in a...

Hi, Without using l'hopital, how may I show that sin[(10pi)/(n+1)^2] / sin[(10pi)/n^2] converges?

Homework Statement Game of Head & Tails between 2 people. The first one to 8 is the winner. If the game is interrupted: when one person has 6 wins and the other has 4 wins, how should the prize money be split? 2. The attempt at a solution The obvious answer (at first) i got is 3:2...

In the figure below, a damped simple harmonic oscillator has mass m = 300 g, k = 95 N/m, and b = 70 g/s. Assume all other components have negligible mass. What is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles (Adamped / Ainitial)? I...

Homework Statement Planet X has a radius double of Planet Y. Planet X also has a mass that is double planet Y. How do the surface gravitational fields of X and Y compare? Homework Equations g=GM/R The Attempt at a Solution So because were looking for the ratio of gx to gy, we can use...

∞ Ʃ (((n)!)^3)/(3(n))! Use the ratio test to solve n=1 So first i put it into form of (n!)^3/3n!, then applied ratio test. from ratio got ((n+1)!)^3/(3n+1)! times (3n)!/(n!)^3 from here I am on shaky ground i go reduce the terms to (n!)^3(n+1)^3/(3n!)(3n+1) times...

I am trying to understand something in the proof of the ratio test for series convergence. If a_{n} is a sequence of positive numbers, and that the ratio test shows that \lim_{n→∞}\frac{a_{n+1}}{a_{n}} = r < 1, then the series converges. Apparently, the proof defines a number R : r<R<1...

1. Let’s say we have a solid wheel. The wheel can be modeled as a disk. Imagine that instead, the wheel is rotated at a location location 0.47R from the center of the wheel, so that the wheel rolled around a kind of loop. Essentially, the CM goes around the dashed line in the drawing. R is the...

Hi everyone. In a proof I'm working on, I have a ratio of two sums of functions in the following form: \frac{f_1(x)+f_2(x)+...f_n(x)}{g_1(x)+g_2(x)+...+g_n(x)} I want to prove this ratio is monotonically increasing in x. All of the functions f_i(x) and g_i(x) are positive and also...

i have been given ap project by my teachers to show the ratio between velocity and torque . i.e i have to show the gear ratio in my project. can some one tell me whether the ratio b/w torque and velocity remains constant if we use different number of gears . also if some one can give me any...

Homework Statement Use the ratio test to find the radius of convergence and the interval of convergence of the power series: [[Shown in attachment]] Homework Equations an+1/an=k Radius of convergence = 1/k Interval of convergence: | x-a |∠ R The Attempt at a Solution I...

Hi all, I always wondered if the combination of gears used to achieve a specific gear ratio mattered. Assuming the desired gear ratio is 3:1, would it matter if the gears used were 10x30 or 9X27? Thanks in advance.

Homework Statement A mineral slurry contains 3 components, solids, liquids and toluene. The slurry has 20 wt% solids and 80 wt% liquid. In the liquid portion of the slurry the mole ratio of toluene to water is 1:5.67 Determine the composition of the slurry (solids, toluene and water) in...

http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w09_qp_31.pdfHomework Statement 6i Homework Equations r=a+λb The Attempt at a Solution first i find AB which is (2,2,-2) the equation if line is then...

I have a linear recurrence sequence and am having a problem understanding what to do when the ratio does not seem to be the same between each of the terms, so Terms; 4, 1.4, 2.44, 2.024... (n = 1,2,3...) How do I find a the ratio of these terms, and if there is none, please advise how I...

How is charge/mass ratio derived in this example?? Hello, I know there are many ways to derive an expression for "q/m", but I am having some troubles with this one. We are given: (1/2)mv^2 = qV (mass, velocity, charge, voltage) qvB = (mv^2) / r (charge...

Homework Statement Hey guys a problem similar to this is going to be on my exam on Thursday, and I'm a bit stuck. A wire of length L and cross-sectional area A, has resistance R. What will be the resistance Rstretched of the wire if it is stretched to twice its original length? Assume...

Homework Statement A stationary detector measures the frequency of a sound source that first moves at constant velocity directly toward the detector and then (after passing the detector) directly away from it. The emitted frequency is f. During the approach the detected frequency is f'app...

There is a certain equation relating both Mp (max. overshoot) and damping ration. Which is; Mp = e(-ζ*pi)/(1-ζ2)1/2 What I get from that equation is for every system a certain damping ratio will result the system in a certain amount of max. overshoot. That sounds ridiculous, because...

Homework Statement Gerald stands on the roof looking up at the full moon, which has a mass of 7.39 x 10^22 kg. At this moment, Gerald is 3.77 x 10^8 m from the center of the moon. If the mass of the Earth is 5.96 x 10^24 kg, and the radius of the Earth is 6.39 x 10^6 m, what is the ratio of...

Homework Statement Does anyone understand why density would increase when the poisson ratio is greater than 0.5 as indicated in this slide from my professor: Does this density increase apply to a system undergoing tension or compression or both?

what do u mean by gamma ray branching ratio of 'k-40' is 10.67%?

Hi guys, I am building my own automated Guided CART, using two car wiper motors as my mian motors connected to bicycle wheels, now i want to know how I am going to determine the weight limit that i can put on my vehicle? the power of the car wiper motors are not yet determined

Homework Statement I attached a file that includes the author's solution, and some of my work. Homework Equations The Attempt at a Solution

Homework Statement Please see the attached. Q1.Why 0° is not a solution of the equation cosθ = 2sinθ - 1? What's wrong with my steps? Q2:http://www.wolframalpha.com/input/?i=cosx+%3D+2sinx+-+1 From the graph,the x-coordinate of the intersection point does NOT equal to the answer...