Unit Definition and 1000 Threads

Homework Statement Its not homework anyway: I'm asked to find the solution to the differential equation: i'' + 2i = f(t) i'(0)=i(0)=0 f(t) = u(t-10) - u(t-20) Unit step function (I've found in part a of the question) Then I've gotten: \mathscr{L}(i) =...

Homework Statement Question 3 (a)A long metal cylinder of radius a has the z-axis as its axis of symmetry.The cylinder carries a steady current of uniform current density J = Jzez. Derive an expression for the magnetic field at distance r from the axis,where r<a. By resolving the...

Find h[n], the unit impulse response of the system descrived by the following equation: y[n]+3y[n-1]+2y[n-2]=x[n]+3x[n-1]+3x[n-2] Can this be rewritten as?(n-->n+2) y[n+2]+3y[n+1]+2y[n]=x[n+2]+3x[n+1]+3x[n]

Homework Statement a particle with charge -2.00 C initially moves at v = 1.00 i^hat + 7.00 j^hat. If it encounters a magnetic field B = 60.00 k^hat T, find the force on the particle Homework Equations F = Q (v x B) The Attempt at a Solution I set up a matrix to find the cross...

Homework Statement let f be the function defined in the region |z|<1 , by f(z)=z^5. prove that f is uniformly continuous in |z|<1...where z is a complex number Homework Equations The Attempt at a Solution

Homework Statement find the Fourier transform of complex exponential multiplied to a unit step. given: v(t)=exp(-i*wo*t)*u(t) Homework Equations ∫(v(t)*exp(-i*w*t) dt) from -∞ to +∞ The Attempt at a Solution ∫([v(t)]*exp(-i*w*t) dt) from -∞ to +∞...

Homework Statement A uniform beam, supported by a uniform strut, is loaded as shown in Figure (Attached). Using the unit load method, determine the value of the vertical deflection at C. BEAM: E = 205 kN/mm2, I = 90 x 106 mm4. STRUT: E = 205 kN/mm2, A = 1500 mm2. Homework Equations...

unit step function u(t) does not contain any transient signal

1. Show that S:= {(x,y)an element of R^2 : x^2 + y^2 =1} is connected. 2. Relevant theorems 1. Path-connected implies connected. The Attempt at a Solution Define f: [0,2pi] --> R^2 by f(x) = (cos(x),sin(x)). This map is continuous, and its image is S^1. The interval [0,2pi]...

Ok- I am teaching trigonometry to low level students right now and I am trying to figure out why they need to know the unit circle. Are there some interesting things they can learn about by using a unit circle? So far, we pretended it was a magic-barbie-sized-half-underground-ferris-wheel...

What is the laplace transform of a function that is 1 from 0 to 10 and 0 elsewhere? I know that this can be represented by the step function U(10-t)U(t)...but how do i find the laplace transform of this?

So in this engineering course I do at my university called Statics, we often use a unit of lb per ft as a unit of force when calculating moments. However, I was just watching an episode of Big Bang Theory when Sheldon said something about a common mistake being when people use lb per ft as a...

How is the distance between any two layers in a FCC unit cell equal to a/√3, where a is the edge length? I think it should be a/2 because the distance of a face centered atom from any 4 edges surrounding it is a/2. Can someone explain it geometrically?

Hey guys, do any of you know of a transmitter/receiver device that can let you know the distance between them? I really need some help fast and would really appreciate it!

Homework Statement I am given this parametrization of the mobius band: F(s,t) = (cos(t)+s*cos(t)*cos(t/2), sin(t)+s*sin(t)*cos(t/2), s*sin(t/2)) Let F1 be F restricted to (0,2*pi) X (-1,1). Let F2 be F restricted to (-pi,pi) X (-1,1). let N1 be the unit normal field determined by F1 let...

hi everybody i need to design a temperature control unit that works in acordance to light, ie: when there is minimal light then the heating element must come on, and when there is lots of light the heating element must go off... these are the following specs of the design: -555 timer must...

I need to obtain the mass per unit length. Is it as simple as just mass / length?

Hi, I have been told that in R^2 the unit circle {(x,y) | x^2 + y^2 = 1} is smoothly mappable to the curve {(x,y) | x^4 + y^2 = 1}. Can someone please tell me what this smooth map is between them? I can only think of using the map (x,y) --> (sqrt(x), y) if x is non-negative and (sqrt(-x), y)...

Homework Statement A sample of dry air has initial pressure p1 = 1000 hPa and temperature T1 = 300k. It undergoes a process that takes it to a new pressure p2 = 500 hPa with unchanged temperature T2 = T1. Compute the mechanical work per unit mass performed by the sample under the following...

Aluminum has a density of 2.699 g/cm3 , and the atoms are packed in a face-centered cubic crystal lattice. Find the mass of a unit cell. -----I already know the answer is 1.792*10^-22g/unit cell I have a question about how you get the answer: I know you multiply 4.480*10^-23g * 4 atoms/1...

Homework Statement Essentially I'm working out a problem and I am given \alpha = \frac{15cm\bullet m^{3}}{\mu C} and I need to get it in just terms of meters/coulombs I'm having a real tough time with weird unit conversions like this. Homework Equations 1m = 100cm 1 micro coulomb = 1 X...

How to transform Ry unit of Energy to Hartree?? Hi How to transform Ry unit of Energy to Hartree??

Three unit vectors v1 v2 and v3 are in R^n. We are told that v1 dot v2= v1 dot v3=1/2. What are the possible values of v2 dot v3. What could the angle be between the vectors v2 and v3 give example for the cases in R^2 and R^3. costheta = (x dot y)/((magnitude of x)(magnitude of y) I...

Physics Grade 12 HELP! Electricity Unit I have attached the question paper with this post Homework Statement v=2 x 10 ^ 5 m/s Volatage=250 or 500? Constants Given: Coulombs constant = 9 x 10^9 Charge of proton/electron = 1.6 x 10^-19/-1.6 x 10^-19 Proton rest mass 1.673 x 10^-27 kg...

Homework Statement Find the unut impulse response h[n] of this system y[n+1]+2y[n]=x[n] Homework Equations I have no clue on how to slove this problem, som pointers would be nice. Thx

hello, I am trying to bin the unit sphere so that each bin has approximately equal area on the sphere. I hope binning the azimuthal angle (0...2*pi) to equal bin widths. Then i need to bin the polar angle(0...pi) so that at poles(angles close to 0 and pi) bin widths are large and close to...

Homework Statement The Dirac function (unit impulse) is defined as \delta(t) = 0 where t \neq 0 the integration of d(t) between -ve inf and +ve inf is 1. Now I picture this as a rectangle with no width and infinite height. In fact I think of the width (along the x axis) as (1/inf =...

If a cubic box(all sides the same length) has a volume of 1.0 L, what is the length of each side of the box? (L= Liter) V= l x w x h or in the problem V=s^2 So I did: 1.0 L^(1\3) = s^3(^1\3) so I got each side to = .33 What I am confused about is what unit is normally...

I am just trying to understand exactly what luminosity per unit frequency is. I know that luminosity (L = 4PI(r2)(flux)) is amount of energy per unit time, but not sure what it means when it is also per unit frequency. The question has a cosmic source of 100 solar luminosity, all emitted...

Homework Statement Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2...

Here's the problem I've been having difficulty with: Find a vector with a magnitude of 1.00 that bisects the angle between the vectors 5.00i + 11.0j and 2.00i − 1.00j. Give your answer in rectangular coordinates. Someone else had posted this same question before, but the answer that was...

If I have the fractional coordinates of asymmetric unit and I know the space group of certain material, is there an easy way to generate the fractional coordinates of the atoms in the conventional unit cell?

Homework Statement I need to show that the unit step function (\Theta(s) = 0 for s<0, 1 for s>0) can be written as \Theta(s)=\frac{1}{2\pi i} \int_{-\infty}^{\infty} dx \frac{e^{ixs}}{x-i0}. Homework Equations - The Attempt at a Solution Firstly, I'm unsure about what "x-i0" actually...

Homework Statement Given that a = (-1,16,-1) and b = (-18,-15,-15), find the unit vector which is perpendicular to the plane containing a and b. There are two possible answers. Choose the answer with a positive x component. Homework Equations (a*b) = (a2*b3-a3*b2)i -...

Homework Statement An electric charge e which moves through a material of permeability μ with a velocity v, produces a magnetic field β at a point r given by: β= ((μ*e)/(4*∏))*((v*ru)/(|r|)2) where ru is a unit vector in the direction of r. Find β if v=4i+3j+3k and r=4i+7j+5k. Take...

Can polar co-ordinate system only be defined in a "background" Cartesian co-ordinate system? What I'm confused about is this: the definition of the polar unit vectors or the polar basis is in terms of the parameter theta. Now, before we go about defining our basis we need to define this theta...

Homework Statement Find a unit vector (a) parallel to and (b) normal to the graph of f(x) at the given point. Then sketch a graph of the vectors and the functions. Function: f(x)=xx Point: (3,9)Homework Equations The Attempt at a Solution...

The book talks about a unit circle... 360 deg = 2(pi) rad if it wasnt a unit circle... say r = 4 would it then be 360 deg = 8(pi) rad?

Homework Statement consider the family of complex mappings: z -> Ma(z) = (z-a)/(áz-1) (a constant) (á is complex conjugate of a) Show that Ma(z) maps the unit circle to itself.Homework Equations the solution should look something like this i guess: Ma(ei*alpha) = ei*alpha The Attempt at a...

1. In an air conditioning unit fresh air at 10°C is mixed with warm air at 30°C. If the mass flowrate ratio of warm to fresh air is 1.6, estimate the temperature at which the mixed air leaves the air conditioner. State any assumptions made. and also do you always make the air standard...

Find a vector with magnitude of 1.00 that bisects the angle between the vectors 5.00i + 11.0j and 2.00i - 1.00j. Give your answer in rectangular coordinates. I'm not going to lie, I am terrible at physics and I had no idea how to solve this question, so I asked someone for help. I came out...

Homework Statement r(t)=ti+t^2j Find the velocity, speed, acceleration, unit tangent, and unit normal vectors.Homework Equations Velocity=r'(t) Speed=magnitude of r'(t) Acceleration=r''(t) Unit tangent=r'(t)/magnitude of r'(t) Unit normal=d/dt[unit tangent]/magnitude of d/dt[unit tangent]The...

Homework Statement Choose a point in the unit axis, say x.Let Y be the distance of that point and the point where thε perpendicular line crosses the unit circle. Find the density and cumulative functions of Y. Homework Equations Basic trigonometry i guess. The Attempt at a Solution...

Does anyone know the (x,y) solutions on the unit circle for 15, 75, 105, 165, 195, 255, 285, or 345 degrees?

H(x,y)=<x^2/4,y^2/9,xy> the region E is 9x^2+4y^2<=36 also wat is given is the work is counterclockwise on R=<2cost,3sint> from -pi<=t<=pi wat the questions are what is the unit tangent the outward normal vector with respect to the region E in terms of t. for the unit tangent i think its...

Hi, I'm not really understanding how to convert the piecewise heaviside into a single function. This was on our quiz and the professor didn't really explain how he got the answer. I can't get the tex to work so: f(t)= { 0, 0 <= t < 1 { (t-1) 1 <= 2 { 1, t >= 2 The answer is...

Homework Statement Calculate dhkl and vc for the (111) direction of germanium. Homework Equations dhkl=a/sqrt(h2+k2+l2) vc=unit cell volume=a1dot(a2xa3) or vc=structure form factor/density The Attempt at a Solution dhkl=a/sqrt(3) I know how to solve this, I've just...

Find Unit Vector perpendicular to the Surface, x3+zx=1 at the point P=(1,2,-1) I figures that the perpendicular vector would be, N(X)=grad(x3+zx) = (3x2+z, 0, x) N(P)= (3,0,1) Then the unit vector would be, n=N(P)/||N(P)|| n=(3/51/2,0,1/51/2) The answer i get is not the...

greetings in a scalar gradient why does the unit vector has appeared?scalar gradient only represent the change in that scalar quantity along x,y and z axis.then why unit vector along x, y and z comes in picture? advanced thanks.

Homework Statement water flows into a tube with a diameter of 6.35 cm at 0.012 meters cubed per sec. it exits the nozzle with a diameter of 2.2cm at what speed? Homework Equations a = pi r squared A1V1 = A2V2 The Attempt at a Solution My question is should i convert the cm to...