deriving Definition and 962 Threads

Homework Statement Derive equation: S=W-W2/ W-W1= M/M1-M2 Homework Equations The Attempt at a Solution

Homework Statement Please see attachment for block diagram of the system. Starting with the block diagram given in Figure 2 derive an expression for the overall transfer function of the system, where Gc(s) is in the form given by Eq. (1). Show that the system is a Second Order system...

Consider heat flow in a long circular cylinder where the temperature depends only on t and on the distance r to the axis of the cylinder. Here r=\sqrt{x^{2}+y^{2}} is the cylindrical coordinate. From the three dimensional heat equation derive the equation u_{t}=k(u_{rr}+\frac{u_{r}}{r}). My...

Hi. We are given a table containing values of mass(m) and time(t). We have been asked to plot graphs of (m) against (t) and then log(m) against (t). The question is: FROM YOUR GRAPHS, DETERMINE THE FUNCTION FOR THE RATE OF DECAY. Of course i know the formula but have no clue how to...

On this page http://www.patent-invent.com/electricity/inventions/special_relativity_1.html you are given that in a certain scenario -(cT)2 = (vt)2 - (ct)2 then it says Hence: t=\frac{T}{\sqrt{1-v^{2}/c^{2}}} But this doesn't rearrange to that equation, and I don't like taking formulae...

Homework Statement The phase velocity of ocean waves is \sqrt{\frac{g\lambda}{2\pi}} , where g is 9.8 m/s2. What is the group velocity?2. Homework Equations v_{p} = \omega/k v_{g} = \partial\omega/\partial kThe Attempt at a SolutionSo I've been trying to find omega and k from the equation in...

Homework Statement Derive algebraic expressions for the range and total time-of-flight of a projectile launched with initial speed v, from a height h, and at an angle Q, above the horizontal. We were given the final equations but I am unsure of how to derive them. Homework Equations...

Homework Statement Derive algebraic expressions for the range and total time-of-flight of a projectile launched with initial speed v, from a height h, and at an angle Q, above the horizontal. We were given the final equations but I am unsure of how to derive them. Homework Equations...

Homework Statement To state the differential form of the Helmholtz thermodynamic potential and derive the corresponding Maxwell's relation. Homework Equations Stated within the solution attempt. The Attempt at a Solution Helmholtz function: F = U - TS Calculating the...

So in one of my classes, we very non-rigorously derived the 1D stress field for a bar with a longitudinal surface loading T(x) like show below: By taking out a differential element (assuming constant cross-sectional area) and applying good old Newton's Second, we end up with: A...

Homework Statement A thin beam of length L (flexural Stufness EI, cross-sectional area A, density p) is connected to a linear spring of stiffness K_s at each end. Derive the governing equation for the natural frequencies of transverse vibrations from the beam equation and boundary conditions...

Homework Statement I'm supposed to show that the Lindhard dielectric functions gives a contribution to the effective potential of a metals as U_{eff}( \vec{r} ) \propto \frac{cos( 2 k_{F}r)}{r^{3}} in the limit of r\rightarrow\infty for d = 3 (3 dimensions) Homework Equations...

derive Coulombs law of electrostatic force by using virtual photon exchange theory of electrostatic field

Alright, so I have a few questions. a) Consider a moon of mass m orbiting a planet of mass M in an elliptical orbit. The equation for the radius of an elliptical orbit is r=a(1-e2) / (1+ecos\vartheta). Derive equations for the orbital radius of the moon when it closest to and farthest from the...

Homework Statement Basically just to find moment of inertia of a spherical shell Homework Equations Moment of Inertia = Int(r^2 dm) The Attempt at a Solution I am in 12th grade and don't know much about integrals? Did I get lucky or am I right? I = Int(r^2dM) dM= (phi)(dA)...

Homework Statement Projectile A is launched horizontally at a speed of 20. meters per second from the top of a cliff and strikes a level surface below, 3.0 seconds later. Projectile B is launched horizontally from the same location at a speed of 30. meters per second. Approximately how...

Hello, I have encountered an exercise in my differential geometry book: to derive the parametrisation and the cartesian equation of the curve witch of Agnesi. To see how it is constructed please see: http://en.wikipedia.org/wiki/Witch_of_Agnesi" How would one derive the results? I am...

Homework Statement Derive equations (5) and (6). Calculate at what angles the time and range are maximized. (5) t= ((2 * Vo) / g) * sin\theta (6) Range = x1-xo = ((2 * Vo)/g)(sin\theta)(cos\theta)= (Vo^2/g)(sin2\theta) sorry about the confusing format. I'm new to latex and new to this...

In the book "Fundamentals of Physics" by H D Young and Freedman,there is formula about the time period of simple pendulum which uses sine function in a complex way which i think is obtained by series expansion of sine function either by Maclurin or Tayler series. Can anyone please tell me how...

Hi I'm playing around with partitions and have come up with an integer sequence representing the maximum number of partitions of various "widths" that display the following properties: - min values in partition are equal - max values in partition are equal - partitions contain equal number of...

Hi, I would like to start from the stress energy tensor for the perfect fluid: T^{\mu\nu}=\begin{pmatrix} \rho c^2 & 0 & 0 & 0\cr 0 & p & 0 & 0\cr 0 & 0 & p & 0\cr 0 & 0 & 0 & p\cr\end{pmatrix} where \rho is the mass density and p is the pressure, and I would like to derive the...

Can anyone help? I have to derive eq of motion of a compound pendulum with 3 rotational dof. I know how to do it, for simple pendulum (using Lagrangian's).

Hey guys, Do any of you happen to know how to derive the formula for General gravitational potential energy (not the mgh one) without using calculus? Thanks. Just in case you guys want to know, I'm trying to derive the equation for this: http://xkcd.com/681_large/. I've got most of it, but I...

Hi all, I was wondering if we could go through how we get the time peroid for a spring with a mass m attached to it. The time period is: T = 2pi sqrt(m/k)We know that F = -kx We know the the the acceleration of a spring is always towards the equilibrium point the speed can be measured negative...

Homework Statement This is my first post, so it might not be that great... Anyways, I need help deriving the formula. This formula is pertaining to the doppler effect, and more specifically, to find the frequency of a sound made from an object moving toward/away from you. f2= f1(v/v-vs) or...

Homework Statement Dervie Newton's form of Kepler's third law. decrribing the orbital motion of two stars in circular orbits with masses M1 and M2, separation a, and period P ie. Obtain F=\frac{ G M1 M2 }{ a^2 } From M1+M2=\frac{4 \pi^2 a^3 }{GP^2} Homework Equations Centre of mass...

By using appropriate theorems derive the following statement : a^2 + b^2 + c^2\geq ab + bc +ac

Homework Statement Suppose a particle of mass 0.240 kg acted on by a spring undergoes simple harmonic motion. We observe that the particle oscillates between x = 0.200 m and x = - 0.200 m and that the period of the oscillation is 1.20 s. At time t = 0, the particle is at x = 0 and has...

hi, I am having trouble understanding what happens to the negative sign when i try to derive keplers law. v=d/t where d is the distance around one orbit, so d=2rpi and t is the time for one orbit in seconds which i will call T so v=2rpi/T now using Ep=-Gm1m2/r Ep is gravitational...

There are two blocks of equal mass M that hang from a massless, frictionless pulley. There is a small square block of mass m sitting on top of one of the blocks. When the block is released, it accelerates downward for a distance H until the block of mass m sitting on tip gets caught by a ring...

I'm attempting to derive the moment of inertia for a cylindrical object. I know that I=\int r^2 dm which equals =\int r^2 p dV My question begins here, the derivations I seen pull p out of the integral, which makes sense to do, because in this case it's a constant. p=M/(\pir^2L). So if I...

See attached file: I would like to show theoretically that the first double spring system is equivalent to the second system with only one spring keff. Then I want to derive an expression for keff in terms of k1 and k2. I think this system is in series and therefore keff =1/k1 +1/k2 but...

Homework Statement Taking into account the electrons momentum and relativistic energy prove that W=(m(sub0)^2c^4+p^2c^2)^(1/2) Homework Equations p=(gamma)m(sub0)v; W=(gamma)m(sub0)c^2. The Attempt at a Solution I have tried expanding the relativistic factor...

First of all, let me copy the standard solution from Griffiths, section 2.5, just for the sake of clarity. PotentialV(x) = - \alpha \delta (x) The bound state eigenfunction: \psi (x) = \left\{ \begin{array}{l} B{e^{\kappa x}}{\rm{ (}}x \le 0{\rm{)}} \\ B{e^{ - \kappa x}}{\rm{...

Homework Statement Basically there's a question that I'm doing which asks me to show how to derive: n lambda=d sin theta We haven't learned it yet and so how do you do it? Homework Equations n lambda=d sin theta The Attempt at a Solution Not a clue! Thanks!

Homework Statement Our teacher assigned us this problem of trying to derive and equation from 4 simpler equations and I just can't seem to get the correct answer so I need some help. a= M1g / (1/2)M2+M1 a= acceleration M1= Mass 1 M2= Mass 2 g= gravity R= radius T= tension I= moment of...

I am trying to follow along with the text's derivation of the Bernoulli equation and I am a little confused with a particular line. The images show an elemental streamtube control volume (CV) of variable area A(s) and length ds. We assume that though the properties may change with time and...

Homework Statement I was looking over my notes and there was a part that didn't make sense. It's basically using the Euler's formula (e^{ix}=cos(x)+isin(x)) and the fact that sin(x)=Im(e^{ix}) to find what Σ sin n sums to. It starts out like this: But this part isn't relevant to my...

Homework Statement Homework Equations My notes say: Cos(x+a) = CosxCosa - SinxSina The Attempt at a Solution When I differentiated each term (using the product rule twice on the right side) I got: (d/dx) { Sin(x+a) = SinxCosa + CosxSina } . Cos(x+a) = -SinxSina...

Homework Statement Derive the following: \left(\frac{\partial U}{\partial V}\right)_{T}=T\left(\frac{\partial p}{\partial T}\right)_{V}-p Homework Equations Use the partner equation: \left(\frac{\partial H}{\partial p}\right)_{T}=-T\left(\frac{\partial V}{\partial T}\right)_{p}+V...

does anyone know how to derive this equation regarding the Michelson interferometer: d_m = (m[lambda])/2 where d_m is the physical distance of a micrometer division, m is the number of fringes that crosses a screen given some d_m and lambda is the wavelength of the laser used to create the...

1. All I need to do is derive the 4th equation of motion being v2= v02+2aD from the second (t=(v-v0)/a) and third (D=1/2at2+v0t). 2. In this case D= (Ending-initial distance) V0= Initial Veolocity 3. By having the second equation solved for t I could substitute it in an completely eliminate time...

Homework Statement Use Kepler's Third Law and a Taylor expansion to derive the following approximation for the orbital period of a satellite in low Earth orbit with a constant height h above the surface of the Earth. h << R_earth : P \approx P_{0}(1+3h/2R_{e}) Homework Equations Kepler's...

Expanding exp(hc / lambda*k_b * T) by Taylor series = 1 + hc /lambda*k_B * T +... But don't you take the derivative with respect to lambda? So I don't get how it would be this.

Hey all, (As I mentioned in my previous post) I am trying to derive the Hamiltonian for a aeroelastic system, where the dynamical equations of motion (determined by Newtonian Mechanics) are known. My process has been to 1. "guess" a form of the Lagrangian, check that it recreates the...

Homework Statement It's been a while since I've done derivatives. I'm working on a physics problem and can't seem to get the correct derivate for a function of the following form: f(x)= A [1+9x^2(x-4)^2]^1/2 A is a constant. The Attempt at a Solution I've tried various ways of...

Hi all, I am in a bit of a dilly of a pickle of a rhubarb of a jam with determining the Hamiltonian of a specific system. For background information it is an 2-DoF aero-elastic system where I am (temporarily) neglecting the aerodynamic lift and moment terms. Being an intrinsically...

Hi all, I'm following along the derivation of the field equations for f(R) gravity, and there's one step I don't understand entirely. There's just something in the math that's eluding me. So wiki has a pretty good explanation...

I've seen the derivation of Dirac Equation using Inhomogeneous Lorentz Group in L H Ryder's QFT book.Can anybody give some comprehensible descriptions of this method?

Hey. I've been having some trouble getting through Mohr's circle. The googles that I've found haven't been too useful. I've seen several questions of the same calibre and what I generally need is how to derive the magnitude/direction of the principal strains as well as the principle stresses...