First order Definition and 546 Threads

Hello, I have a question on a the units of a first order system's time constant. If i have a first order system the basic transfer function will be: K/(tau*s+1) where K is the Gain, and tau is the system's time constant. tau's units, according to what I've learned, are [sec]. but...

Could someone explain what the 'first order' diffraction peak is?

Hello! I would like to prove the following statement: Assume f\in C^{1}(\mathbb{R}). Then the initial value problem \dot{x} = f(x),\quad x(0) = x_{0} has a unique solution, on any interval on which a solution may be defined. I haven't been able to come up with a proof myself, but would...

Solve the first order hyperbolic equation 3 du/dx + 2x du/dt =2u With initial condition: u(x,0) = 2x+4 My attempt at a solution I usually adopt the method of characteristics: dx/a = dt/b = du/c So from the above: a=3, b=2x and c=2u am I on the right track here?

Hello all, I don't have much experience with ODEs. I have a simple system, which I believe is first order linear, similar to the following: dA/dt = 2A + 3B - C dB/dt = A + 2B - C dC/dt = -2A + 5B - 2C Now I would like to include the constraint that A + B + C = 1. How do I do this...

2r(s^2+1)dr + (r^4 + 1)ds = 0 2.book answer different than mine...book's answer: r^2 + s = c(1 -r^2 s) 3. 2r(s^2+1)dr =- (r^4 + 1)ds -2r/r^4+1 dr = 1/s^2+1 ds int -2r/r^4+1 dr = int 1/s^2+1 ds with u substitution on left we have u = -2r, etc. tan^-1 r^2 = - tan^ -1 s + c tan^-1 r^2 +...

Homework Statement I haven't done ODEs in a few years and I am trying to do this equation: m_{Hg}C_{p,Hg}\frac{dT_{Hg}}{dt} = Q Q = hA(T_{air} - T_{Hg}) T_{Hg}(t = 0) = 20 I need to find T_{Hg}(t=590) Homework Equations The Attempt at a Solution h, A, m_{Hg}, C_{p,Hg}...

The circuit is in the attachment, plus the values that I've managed to find out so far. Im having problem with figuring out the voltage at t=infinity. So far i know that when t->infinity that inductors become short circuit. It says to apply current division and then Ohm's Law as a hint, and...

dy/dt + y = \infty \sumSin(nt)/n^2 n=1 Ok still a bit new with all these symbols and stuff but that is the basic jist of it. y(t) = yh(t) + yp(t) it what i thought about using to start off with, yh(t) = Acos2t + Bsin2t. Then subbing yp(t) into the differential equation. Not really...

dy/dt + y =\infty\sumn=1Sin(nt)/n^2

dy/dt + y = Sigma Sin(nt)/n^2

Hi, I am trying to calculate the first order photon self-energy. At a point, I must calculte the following integral : \int d^4k \frac{(k+q)^\mu k^\nu+(k+q)^\nu k^\mu - g^{\mu \nu}(k \cdot(k+q) - m^2}{k^2 + 2x(q\cdot k) + xq^2 -m^2} I know that I must wick rotate and that k^2 will...

I have the following equation:: xy' = y + 2*sqrt(xy) I know I should either use the F(y/x) substitute or Bernoulli's method of substitution but I'm not sure how to manipulate the equation to determine which it is. If someone had some helpful tips on how to start, please let me know...

Homework Statement A first-order system G(s)=\frac{k}{s+a} and its response to a unit step input are shown in the figure below. Determine the system parameters a and K 2. The attempt at a solution I’ve tried to find K & a using MATLAB and read a lot but didn’t find...

Hi, I'm confused with the solution given for this practice problem. All of these components are said to be in parallel, yet the current is worked out only across the resistors. I thought the inductor would be a short circuit to DC. Am I looking at this backwards, is it modelling the inductor...

Homework Statement How do you use the Quadratic Formula to solve First Order ODE? For example, I am given this integration (see attachment at the bottom). Homework Equations The Attempt at a Solution I integrated both sides but I do not know where to go from there (see attachment at the...

I am to find a general solution of the system of problems below. I have done so for x(t) but am unsure how to find it for y(t)... x'=y, y'=-x x''=y=-x x''+x=0 Characteristic eq: r^2 + 1= 0, r = +/- i x(t) = A cos(t) + B sin(t) How do I go about calculating y(t), which th book shows as...

Homework Statement A security alarm for an office building door is modeled by the circuit [below]. The switch represents the door interlock, and v is the alarm indicator voltage. Find v(t) for t>0 for the circuit [below]. The switch has been closed for a long time at t=0-...

Homework Statement Find the voltage drop across the capacitor just after the switch is opened v(0+) Most variables are in picture attached C = 100mF Homework Equations Vc(t)= Vc(\infty)+[Vc(t+)-Vc(\infty))*e-(t-t1/\tau) The Attempt at a Solution First i assumed that the...

Homework Statement I am stuck on these two questions. The first one I can start off and finish but i cannot do the middle part and in the second question I have no idea how to start it off. Find the general solution of the following separable equations; then use the solution which obeys...

http://img713.imageshack.us/i/39642770.jpg At time t = 0_ The circuit looks like the voltage source in series with R1 and R2 with the inductor acting like a short circuit. iL (0_) = 60V/50Ω = 1.2A At t = 0+ The circuit looks like http://img839.imageshack.us/i/52735488.jpg...

Hi, I have the differential equation \left(\frac{df}{dr}\right)^2-\frac{1}{r-1}\left(1+\frac{1}{4r^3}\right)=0, does anyone know how to attack this? (I'm led to believe this is only possible if r>1, not sure why not r<1, although I can see it does blow up at r=1) thanks

Homework Statement Convert the equation to a first order system. d^2y/dt^2 + 3dy/dt + 2y = 0 The Attempt at a Solution Set d^2y/dt^2 = dv/dt dy/dt = V So, I now have: dv/dt + 3v + 2y = 0 Now, I'm not sure what to do with that Y, In my notes we only did examples with...

http://img39.imageshack.us/img39/2991/captureucm.jpg Attempt to solve: omega = 1/R2C1 ; omega = 2pi*f so C1 = 1/R2*2pi*f , where f = 1000Hz so C1 = 0.53 nF (nanofarads) then Ao = -R2/R1, so absolute value is 15 gain V/V? in terms of dB its approx 23.52dB using 20 log X...

Homework Statement I need to resolve this network and find the equation for voltage at some time, t'>0. I know how to find the equation, but I'm having trouble finding the value for tau because I'm not sure what the equivalent resistance is. Homework Equations tau = R*C R1 = 4 k...

Homework Statement What subsets of the real line R are definable in (R,<)? What subsets of the plane RxR are definable in (R,<)? Homework Equations A subset is definable if there is a formula in first order logic that is true only of the elements of that subset. For example, in the...

Homework Statement dy/dx=y-e-x Homework Equations none The Attempt at a Solution According to Wolfram Alpha the solution is y = cex+.5e-x . I tried multiple approaches, but I cannot obtain this answer. I can't figure out what step 1 is. I tried factoring out e-x from the right...

I am trying to solve a problem (not homework, too old for that! lol!) which involves the time dependent schrodinger equation for magnetic moment in time-dependent magnetic fields. I end up with the following that needs to be solved: x' = -i*(b*t-a*t^2)*x - i*c*y y' = -i*c*x -...

dv/dt=g-(k/m)*v^2 i thought about all sorts of diff eq solving techniques but nothing comes up to my mind dv/(g-(k/m)*v^2)=dt but it doesn't really help ...

Homework Statement The equation for the velocity of a falling parachutist can be computed by, v(t) = \frac{gm}{c}(1-e^{-(\frac{c}{m})t}) Use a first-order error analysis to estimate the error of v at t = 6, if g = 9.8 and m = 9.8, c = 12.5 plus or minus 1.5. Homework Equations...

Homework Statement Solve the diferential equation: dx/dt + Rx^2 + G = 0 G constant = 10^18 R constant = 10^-10 Initial conditions x(0) = 10^8Homework Equations what approach to take? The Attempt at a Solution First I try to apply bernoulli, but since in this equation I do not have a term...

Homework Statement t^2 y' + 4ty - y^3 = 0 Homework Equations Hint was given in the question: substitute with v = y^-2 The Attempt at a Solution Dividing by t^2 and isolating y': t^2 y' = y^3 - 4ty y' = y^3 / t^2 - 4y/t dv/dt = 0 y = v^(-1/2) dy/dt = (-1/2)v^(-3/2) v' so...

find the solution for the following equation: dy(t)/dt + 3y(t) = x(t-2), t > 0 and y(0) = 0 i did it by parameterization but am unsure if it is correct. i need help especially with the limits of integration. y' + 3y = x(t-2) yh' = -3yh yh = Ce^-3t y(t) = v(t)e^-3t (ve^-3t)' =...

Homework Statement Going over and over the perturbation theory in various textbooks, I feel that I've NEARLY cracked it. However, in following a particular derivation I fail to understand a particular step. Could anyone enlighten me on the following? Multiply |\psi^{1)_{n}>...

Could anyone help me with this? Donald and Daisy Duck took their nephews, age 4, 5, and 6, on an outing. Each boy wore a tee-shirt with a different design on it and of a different color. You are also given the following information: ■ Huey is younger than the boy in the green tee-shirt. ■...

Homework Statement 11(t+1)dy/dt-7y=28t y(0)=13 Homework Equations The Attempt at a Solution I got µ(x)=1/(t+1)^(7/11) and then used 28/11(t+1)^(7/11)*integral of t/(t+1)^(18/11) dt. And that's where I'm stuck.

Homework Statement Hi, If x^2+1=y/(x-y'), where y'=dy/dx, find dy/dx I have tried so many ways, but I cannot seem to get the correct answer. The answers I have got previously are: i) x² + 1 = y/(x - y') (x² + 1)(x - y') = y x(x² + 1) - y'(x² + 1) = y x(x² + 1) - y = y'(x² + 1)...

I was given the following question Which of the reactions on the right are allowed by first-order processes? For those which are not allowed, state one conservation law which is violated. What is a first order process in particle physics? i.e what does first order refer to? What would be...

Having a bit of trouble, what do i do next? Thanks.

The equation of motion of a rocket with mass depletion during ascent and subject to drag forces can be written as M(t) dV/dt = A - M(t)g - BV^2 (Eq. 1) with initial condition V(t=0) = 0 (V is velocity and t is time) Let us assume a linear mass depletion according to...

A question, if you have a nonhomogenous first order differential equation, can it be solved by using the usual nonhomogenous way, with the arbitrary constants, instead of using the integrating factor?

Homework Statement The initial mass of fish in a lake was 7 thousand pounds on January 1st, 2001. Since the time, there was a 4-year moratorium on the harvesting on this specific type of fish. This species of fish reproduce at a rate proportional to the mass and by next year on the same...

Consider cylindrical coordinates p = (x^2 + y^2)^.5  angle = arctan(y=x). Consider your curve to be specified by z(p). Write down a (first order) differential equation governing z(p) please help!

I must derive the 1/4th life expression for a first order rxn. ln(\frac{[A]_{\circ}}{[A]_{t}})=kt ln(\frac{[A]\circ}{\frac{1}{4}[A]_{\circ}})=kt_\frac{1}{4} ln(4)=kt_{\frac{1}{4}} do I set t=1/4 ? \frac{ln(4)*4}{k} \frac{5.545}{k} What am I doing wrong here? The answer is allegedly...

Consider a certain linear system of 2 equations x'=Ax. Suppose the real-valued coefficient matrix A has r=-1+4i as one of its eigenvalues, and that one of its corresponding eigenvectors is (2, 5-2i). Find the particular solution that satisfies the initial condition x(0) = (-4, 3)...

first order system DE --> second order Homework Statement Find a second-order DE for x alone that is equivalent to this system. Homework Equations dx/dt = 2x-y dy/dt = -x The Attempt at a Solution I honestly have no clue where to start; in class we pretty much only stuck to...

Hey, I'm studying Predicate Logic at the moment and I can't seem to wrap my head around the way that english sentences would convert into second order logic. What kind of sentence can be faithfully represented in PL2 but not in PL1? Sorry if this isn't the appropriate section; I'm actually in...

Homework Statement (x+y)dx-(x-y)dy=0 Homework Equations The Attempt at a Solution The solution is c=arctan^-1(y/x)-(1/2)*ln(x^2+y^2) but I don't know how to get the answer. If someone could explain how to solve the above DE, that would be great.

Homework Statement Background: Jack's wife Jill, mindful of the water restrictions is determined to carry buckets of bath water out of the house to water bean stalks. She carries out 18 litres of water on the first day. The amount of water Jill carries out An, in litres on the nth day is...

Homework Statement dx/dt = x - y + (x^2) - xy dy/dt = -y + (x^2) - Determine the critical points for the equation, - Determine the linearized system for each critical point and discuss whether it can be used to approximate the behaviour of the non-linear system. What is the type and...