Derive Definition and 591 Threads

Homework Statement I try to derive the expression of ω with respect to t, but the problem is the armature current Ia or the flux is unknown. I don't know how to solve it. Anyone could give me ideas? Thanks a lotHomework Equations τ=J(ω/t) Vs=IaRa+Ea T=KEøIa Ea=KEøω

Hi guys, I need some help on this question: Derive the van der Waal interaction potential between 2 spheres of radius R_1 and R_2 using the Hamaker approach. Take the distance between the center of each sphere to be D. Thank you very much for your help!

I'm wondering how one solves for the quantum harmonic oscillator using matrix methods exclusively. Given the Hamiltonian \hat{H} = \frac {1}{2m} \hat {P}^2 + \frac {1}{2} m \omega ^2 \hat {X}^2 and commutator relation [ \hat {X} , \hat {P} ] = i \hbar \hat {I} is that enough for premises...

Homework Statement This is a 3 state machine with one input variable. The input given for x produces the output sequence for z. The machine starts in state A. I am asked to derive the state table. x=010001010010010011010 A z=001000000001001000001 Homework Equations The Attempt...

Hello there, If a mass, m, is placed at one end of an boat of mass M, which is located on a frictionless ocean. If the mass, m, is moved from one end of the boat to the other end, conservation of center of mass position ensures that the boat shifts a small distance in the opposite direction...

I'm not sure if I can ask this question clearly, but anyway... We have this collection of 17 or so particles. Some of them have been known to exist for a very long time and were found when physics was still in its relative infancy, because they were trivial to detect and distinguish. I'm...

I need some help with an equation. I will use to find the value of acceleration due to gravity. With a air track and a spring attached to a glider we should find the value of "g". The track is inclined and with two different equilibria (which are achieved by using two different masses on...

So for starters the area of an entire circle has 360º,right? So we can say that: ##1∏r^2## is ##\equiv## to ##360º## So by that logic ##0.5∏r^2## is ##\equiv## to ##180º## And finally ##0.25∏r^2## is ##\equiv## to ##90º## Divide both sides by 9, and you get : ##0.25∏r^2/9## is...

Homework Statement Derive the energy equation for a van der Waal gas when T and v are the independent variables. Homework Equations I'm required to start from: du=\frac{\partial u}{\partial T} dT +\frac{\partial u}{\partial v} dv The Attempt at a Solution We'll when I first...

Homework Statement Actually this is not from homework. It occurs in my brain this afternoon. Is it possible to derive the analytic expression of a function by its Taylor series expansion? For example, given the following expansion, how to derive the analytic expression of it? f(x) =...

It's easy to get a function from a table that follows a clear pattern, but what if the values for y (or x) don't follow a pattern? For example; x = 1 , y = 13 x = 2 , y = 9 x = 3 , y = 3 x = 4 , y = 8 x = 5 , y = 1 x = 6 , y = 5 x = 7 , y = 12 If you look at these points on a graph...

1. For the past 1 hour, I'm trying to derive lens maker's equation using fermat's principle, which of course is our homework. Any help would be great regarding the topic. 2. According to Fermat's Principle, optical path length OPL = PA + AQ, here PA and AQ are two rays. Now using this I...

Guys, My calculus is really rusty and I need help solving this equation using a time derivative (denoted with a dot) in order to get the relativistic equation of motion for the Universe The equation is: adot^2 = Λc^2a^2/3 where adot is the time derivative of the scale factor, lambda...

Is there any way to derive an equation for compound interest based on effective interest rate instead of the nominal interest rate?

Homework Statement Show that the experiment depicted in Figure 2.11 and discussed in the text leads directly to the derivation of length contraction. Figure 2.11: Homework Equations d=v*t Requested result: L=L0\sqrt{1-\frac{v^2}{c^2}} The Attempt at a Solution In K the...

Homework Statement Assume that the center of mass of the Earth moves with approximately constant velocity with respect to the fixed stars, and that \mathbf{\omega}, the angular velocity of the earth, is constant. Rederive the terrestrial equations of motion...

Homework Statement Derive from the uncertainty principle a formula for the relative spread of the spectral line that corresponds to the longest wavelength of the Lyman series. Homework Equations uncertainty principle: σxσp≥\hbar/2 planck constant \hbar=h/2pi h=λp Lyman series...

The calculation for the maximum bending moment is to be verified experimentally using a strain gauge bonded to the outer surface of the beam, at the point where the maximum bending moment occurs. Derive an equation which could be used to calculate the bending moment from the measured strain...

Homework Statement Find the general solution for the current I(z,t) associated with the voltage V(z,t).Do this by substituting [1] into [2] and [3], integrate with respect to time, and then take the derivative with respect to z. Homework Equations V(z,t)= f+(t-z/vp) + f-(t+z/vp) [1]...

The following is the Planck's derivation for black body radiation $${\rho}({\lambda}) d{\lambda}=E({\lambda})*f({E(\lambda}))*D({\lambda})d{\lambda}------equation 1$$ $$\int_0^\infty{\rho}({\lambda})d{\lambda}$$ is the density of radiative energy. From...

Homework Statement The calculation for the maximum bending moment is to be verified experimentally using a strain gauge bonded to the outer surface of the beam, at the point where the maximum bending moment occurs. Derive an equation which could be used to calculate the bending...

This is a revision question rather than homework as I have the answer and working. I have attached the block diagram and first part of the answer which explains how to derive the transfer function from first principles. I understand the principles behind this and how the RHS of the equation...

Homework Statement [/b] The attempt at a solution[/b] I have done the first bit but don't know how to show that phi(r,t) is a solution to the equation of motion.

Homework Statement Hello! I have two graphs which I need to find if there is relationship between them (all in one). I have to create a formula/equation that can show and prove that there is this relationship between them.I am really confused at the moment since I do not know if there is...

Hi there, I'm trying to derive the following equation, but despite internet searching haven't been able to figure out what to do with the multiplier, D. D * dθ/dz + k = C I need to derive the equation and then plot the graph θ(y-axis) against z (x-axis). Any help greatly appreciated...

Hello all, In Carroll's there is a brief mention of how to get an idea about the curvature tensor using two infinitesimal vectors. Exercise 7 in Chapter 3 asks to compute the components of Riemann tensor by using the series expression for the parallel propagator. Can anyone please provide a...

Hi, We have: \beta(a,b)=\int_0^1 t^{a-1}(1-t)^{b-1}dt,\quad Re(a)>0, Re(b)>0 and according to Wikipedia: http://en.wikipedia.org/wiki/Pochhammer_contour we can write: \left(1-e^{2\pi ia}\right)\left(1-e^{2\pi ib}\right)\beta(a,b)= \int_P t^{a-1}(1-t)^{b-1}dt valid for all a and b where P...

Homework Statement Derive from Maxwell's equations these Hill equations for 's' and 'p' mode waves; s\hspace{3mm} modes: E(r,t) = \Psi_{s}(z)e^{i(\beta x - \omega t)}y \\ \hspace{10mm}Hill\, Equation for\, \Psi_{s}(z)\\ \hspace{17mm} \dfrac{d^{2}\Psi_{s}(z)}{dz^{2}} +...

Homework Statement http://imageshack.com/a/img580/682/z3mt.jpg Derive a linear differential equation for the above LTI system. Homework Equations i_C=C\frac{dV_C(t)}{dt} V_L=L\frac{di_L(t)}{dt} The Attempt at a Solution Using KVL, I can get the following equation...

Can someone explain this proof of the moment of inertia of a sphere? And how you can use the same principals to solve for other formulas? https://www.physicsforums.com/attachment.php?attachmentid=62987&stc=1&d=1381895479http:// I understand each individual variable. But I don't understand...

can you show me derive cross product from dot product?

Homework Statement Derive the equation v^2 = u^2 + 2as I have no clue how to do this please can someone help! Thank you!

Homework Statement Derive the differential equation from the following circuit Homework Equations The solution needs to be a differential equation in standard form, so that I can solve the equation for the characteristic modes, zero-input response, zero-state response, etc. The...

Can anyone derive the p.m.f. of Poisson distribution without mentioning the binomial distribution? The binomial deriving method put lambda = np and finally the binomial p.m.f. become the Poisson one as n goes to infinity. It seems that this is only proving that binomial distribution will...

Hi, i am trying to develop a CDF from a given MGF. The standard way of using the inverse Laplace transform etc.. is not feasible due to complexity of MGF. I was woldering if there is another straighforward direction via integration or differentiation method to produce the CDF (or PDF)...

Homework Statement The formula for divergence in the spherical coordinate system can be defined as follows: \nabla\bullet\vec{f} = \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 f_r) + \frac{1}{r sinθ} \frac{\partial}{\partial θ} (f_θ sinθ) + \frac{1}{r sinθ}\frac{\partial f_\phi}{\partial...

Homework Statement Derive he Laplace Transform of the third derivative of f(t). Homework Equations The Attempt at a Solution So, I'm not at all sure how to do this. I think I can start with: L{f'''(t)} = But I'm honestly not sure how this works. Any guidance would be...

Homework Statement 1. (a) Find the equation of the circle with the straight line joining A(1;-1) and C(3; 4) as diameter. (b) Hence or otherwise, derive the general formula (x - x1)(x - x2) + (y - y1)(y - y2)=0 of the equation of a circle for the points A(x1; y1) and C(x2; y2): Homework...

So, I have been trying to figure out how to derive the equation for the surface area of a sphere. All attempts have resulted in colossal failure and as such are not even worth posting on the forum. I know Archimedes was the first to come up with the formula but I have not been able to find...

Homework Statement Begin from the expression of the electric field outside an infinite sheet of uniform surface charge density, E=\frac{σ}{2\epsilon}. Derive the electric field just outside an ideal conductor: E=\frac{σ}{\epsilon}. Do NOT use Gauss's law. Homework Equations Not sure...

hello remember not speak English and use a translator on line, together some pictures to show some errors,from a simple integral or easy to those who are not as oscillatory integrals, when I worked and ask oscillatory integrals or approximate numerical answers, also when try plot a complex...

Homework Statement Use calculus to derive the volume of a pyramid The Attempt at a Solution There's probably a simpler way to go about this, but I wanted a challenge. I decided to calculate 1/4 of the pyramid in the first octant and then multiply my final answer by 4. First we have...

Can't figure out how they're constructed. I'm guessing it would be geometric in nature. It would be nice to be able to derive at least a few of the ones I inevitably forget through disuse. Math level: ordinary differential equations.

Hello All, Is is possible to the derive pitch, roll and translational acceleration, and the location of pitch and roll axes from a set of tri-axial accelerometers mounted on a rigid body? My initial though is that 3 accelerometers might be sufficient, but not sure. I need to do figure out the...

How is \lim_{n\rightarrow ∞} \frac{1-r^{N+1}}{1-r} derived? Is it directly related to S_{n}=\frac{a(1-r^{n})}{1-r}? If so, how does the r^{n} become r^{n+1} and how does the a disappear? I've seen how to derive S_{n}=\frac{a(1-r^{n})}{1-r}, but have never come across...

If one knew the equations for the 5 fundamental forces, would that not explain the entirety of all physical phenomenon in the universe? (Presuming there were not undiscovered forces?) Or would something like quantum mechanics not be explainable via those interactions? Does the nature of the 5...

Hi, I have been reading around about back EMF and their derivations for simple DC motors. However for some reason, the step between obtaining the total emf of the motor from summing the individual emf of the coils is not very clear. For example: Induced emf due to single coil: e = d∅_c/dt...

Happy summer...ish! I am reading the lecture/presentation at: http://fias.uni-frankfurt.de/~brat/LecturesWS1011/Lecture5.pdf In slide two, they outline the Hartree product, but can anyone give a hint about how it's derived, or how to verify it? Put another way, can someone give me...

So I recently learned that you can derive all four of the propositional logic operators (~, V, &, →) from Nand alone. As I have understood it, so long as you have negation, and one of the other operators, you can derive the rest. Like P → Q can be defined as ~P V Q. However, I learned that...

Homework Statement The average energy of a harmonic oscillator is written using Boltzman statistics as: <ε> = (<n> +.5) = \frac{\sum_{n} ε_{n} exp \frac{-ε_{n}}{kt}}{\sum_{n} exp \frac{-ε_{n}}{kt}} Expand the expontentials and hence derive the Planck Occupancy <n> = n(ω,T)...