Second order Definition and 570 Threads

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color] how we can find contact time of second order system ? 2y**+4y*+8y=8x I want to find damping coefficient ... howz possible

I have this second order differential equation but I'm stumped as to how to solve this since the zeroth order term has a Sine function in it and the variable is embedded. ##\ddot y(t) + 3H (1+Q) \dot y(t) -m^2 f \sin(\frac{y(t)}{f}) = 0## ##H~##, ##~Q~##, ##~m~##, and ##~f~## are just...

Homework Statement I need to design a second order filter with unity gain. Homework Equations None - not taking component values into account for now. The Attempt at a Solution Is this a correct method of creating a 2nd order low pass filter with unity gain?

Homework Statement I have this set of equation: My''+Cy'+Ky=0 but C=0 M is a matrix consist of {(-m) (0)/( -1/12mb^2) (-1/12mb^3)} and K is a matrix of {(-K1-K2) (-K2b)/ ((K1b-K2b)/(2)) (-K2b^2/2)} and y is a coordinate system which is (x1,θ) Now i have to convert these...

Homework Statement The harmonic oscillator's equation of motion is: x'' + 2βx' + ω02x = f with the forcing of the form f(t) = f0sin(ωt)The Attempt at a Solution So I got: X1 = x X1' = x' = X2 X2 = x' X2' = x'' ∴ X2' = -2βX2 - ω02X1 + sin(ωt) The function f(t) is making me doubt this answer...

Sorry, I mistakenly reported my own post last time. But later I realized that these limits do work. So, I'm posting this again. I'm using these limits to check second-order differentiability: $$\lim_{h\rightarrow 0}\frac{f(x+2h)-2f(x+h)+f(x)}{h^2}$$ And, $$\lim_{h\rightarrow...

Homework Statement Hi guys, I am have a problem with the question displayed below: [/B] Its 6.1 ii) I am really not sure how I am suppose to approach this. I am new to partials, so any advice would be great. Homework EquationsThe Attempt at a Solution So far I have: $$\frac{\partial ^2...

Homework Statement Hi guys, I am having trouble with ex 6.1 and 6.2. I am listed my ans below, and shown working. Could someone please advise. First I am not sure why I have to start with $$x=Ae^{imt}$$. Why cannot start with $$Ae^{px}$$? Homework EquationsThe Attempt at a Solution i) $$Aux...

Homework Statement A mass ##m## on a frictionless table is connected to a spring with spring constant ##k## so that the force on it is ##F_x = -kx## where ##x## is the distance of the mass from its equilibrium position. It is then pulled so that the spring is stretched by a distance ##x## from...

Homework Statement NOTE - When I post the thread my embedded images aren't showing up on my web browser, but they do show up when I bring it up to edit, so I don't know if other users can see the pictures or not... If not, they're here: Problem outline: http://tinypic.com/r/34jeihj/9 Solution...

Homework Statement I need to solve: x^2y''-4xy'+6y=x^3, x>0, y(1)=3, y'(1)=9 Homework EquationsThe Attempt at a Solution I know that the answer is: y=x^2+2x^3+x^3lnx Where did I go wrong. I was wondering if it's even logical to solve it as an Euler Cauchy and then use variation of parameters...

Can someone please explain to me what it means what they say a model is "first and second order dependence?"

Homework Statement Homework Equations The Attempt at a Solution I have done question 1.18 and I understand it completely. However, for question 2.5, I do not understand how they got G(s)? Why isn't the G(s) in question 2.5 the same as G(s) at the bottom of question 1.18? I asked my lecturer...

The second order ODE is, \begin{equation*} \frac{d^2 x}{dt^2} = -\omega^2_g \frac{dx}{dt} \end{equation*} I tried solving this by substitution of the second order derivative into a variable and transforming the equation into a second order polynomial, and I get the solution involving an...

I am trying to solve this equation: d/dx[dF(x)/dx] = [c(c+1)/x^2)F(x), where c is a constant. Do I still use the characteristic equation to solve this? EDIT: Is it solvable using Dawson's integral rule?

Hi folks, I am reading Poisson's Teatrise on Mechanics. In the introduction he talks about the infinitesimals. Let's say A is a first order infinitely small quantity, a differential of the first order, if the ratio of A to B is infinitely small too it means B is an infinitesimal of the second...

Can the Euler approximation method be used to solve higher order DE? I have ##\ddot x=\omega^2 x## which i rewrite as ##y''=\omega^2y##. initial conditions y(0)=0, y'(0)=1. The Euler method: ##y_{n+1}=y_n+h\cdot y'_n##. i use this to make: $$y''_{n+1}=y'_n+h\cdot...

Homework Statement The ordinary differential equation describing shm is d^2x/dt^2=-w^2x where x is the displacement, t is the time and w is the frequency. If x=0 at t=0, the analytical solution is x=Asin(wt), where A is the amplitude. 1) Rewite equation 1 as two first oder ode's suitable for...

Hello! Im trying to solve this second order differential equation: \begin{equation*} -\dfrac{d^2y}{dx^2}+\dfrac{3}{x}\dfrac{dy}{dx}+(x^2+gx^4+2)y=0 \end{equation*} Any idea? Maybe it could be converted to a Bessel-like equation (?) with an appropriate change of variables. The equation...

Hello, Can someone explain this to me? In the above case ct=yt-gt I tried to solve it as a three variable taylor approximation but got a few extra terms that weren't included in the above. So I am a little confused now. I only need to understand how the first line was derived because I get...

Homework Statement Calculate the second-order correction to the ground-state energy of the stationary states of the system. The perturbed Hamiltonian is: H' =- (/gamma /hbar m /omega)/2 (a+ - a-) ^2 2 & 3. Relevant equatio and the attempt at a solution This is not right. I follow the same...

Homework Statement 2. Consider an electric circuit consisting of an inductor with inductance L Henrys, a resistor with resistance R Ohms and a capacitor with capacitance C Farads, connected in series with a voltage source of V Volts. The charge q(t) Coulombs on the capacitor at time t ≥ 0...

Homework Statement The electric potential energy v(r) of a charged particle located between two uniformly charged concentric spheres with radii r1 and r2 satisfies the second order differential equation rv′′+2v′=0, r1≤r≤r2 where r is the distance of the charged particle from the common centre...

Hello everybody, My question is about nonlinear optic in both macroscopic and microscopic point of view. What is the relationship between second order susceptibility tensor \chi^{(2)} and the first hyperpolarizability tensor \beta ? Thank you everybody. Konte.

Homework Statement Solve y''+(cosx)y=0 with power series (centered at 0) Homework Equations y(x) = Σ anxn The Attempt at a Solution I would just like for someone to check my work: I first computed (cosx)y like this: (cosx)y = (1-x2/2!+x4/4!+ ...)*(a0+a1x+a2x2 +...)...

Homework Statement If I have a closed loop second order transfer function such as: $$\frac{10-s}{0.3s^2+3.1s+(1+24K_{C})}$$ Can I still use this formula for overshoot (when a step input is applied) ?: $$\frac{A}{B}=e^{\frac{-\pi \zeta}{\sqrt{1-\zeta^2}}}$$ Where B is the step input size I...

Hello every one, I have an equation related to my research. I wonder if anyone has any suggestion about solving it? y''+y' f(y)+g(y)=h(x) thanks

Given is the second order equation, ##X_{uv} = A(u,v)X_{u} + B(u,v)X_{v}## defined on a domain ##(u,v)## in the plane. ##X## is a three dimensional vector and ##A## and ##B## are arbitrary smooth functions. When does such an equation determine a surface in ##R^3## and what in general can be...

Homework Statement imgur link: http://i.imgur.com/Bv3qtPm.png Homework EquationsThe Attempt at a Solution From the FBD it is apparent that there is a constraint -k_1x_1 + k_2(x_2-x_1) + 5\cos{10t} = 0 If you combine this with {x}''_1 = -(k_1+k_2)x_1 + k_2x_2 + 5\cos{10t} and m{x}''_2...

I'm supposed determine whether following statements are true or false. However, I can't get past the notation. Question: the second order differential equation $\ddot{x}+\dot{x}+x = 9t$ is: (a) equivalent to $\begin{cases} \dot{x} = y, & \\ \dot{y}=-y-x+9t, &\end{cases}$ (b) solved by...

Hello guys, I'm studying from Green's Function With Applications by Duff, and he finds the general solution(homogeneous sol.) to this differential equation: , but i I've never seen a equation like this before, how can i manage to solve this equation??

So, I had studied oscillatory motion for a while and I found it unpleasant to have to remember the various different solutions for the equations of motion. I began to learn about second order linear differential equations and now I know how to solve this kind of stuff. But there is a problem...

Homework Statement Find a particular solution to ##y'' - 3y' + 2y = 6x^2## I don't understand how/why the value of c has been determined. I'm hoping it is a mistake in the solution, but knowing me, it's probably my mistake. Homework EquationsThe Attempt at a Solution assume a solution of the...

Hi all, hopefully this is in the correct section here. Any help is really gratefully received. 1. Homework Statement I have a coursework, one question asks us to use a 2nd order approximation of the transfer function to..."estimate the settling time (5% of the settling value of output, peak...

i am given an equation which i have to solve in simulink. the equation is quite veered to me. some one help me in understanding what kind of equation it is so that i can solve it in MATLAB simulink. (2+x^2)theta'' + (2xx' +1)theta' + 9.8(xcostheta-sinthetha)-x''=T

Homework Statement Solve the following differential equation and compare computer solutions \begin{equation*} 4y''+12y'+9=0 \end{equation*} Homework Equations None The Attempt at a Solution [/B] First of all looking at this equation, even though it is in the section where we learned about...

Hi, it is known that second order correlation function (g2) is a constant( =1) for ideal laser or single frequency light sources. So, what is the second order correlation function for non ideal laser? Is it still a constant or something related to the coherence time of the laser?

I know how to solve \frac{d\vec{u}}{dt} = A\vec{u}, I was just watching a lecture, and the lecturer related that solving that equation is pretty much a direct analogy to \vec{u} = e^{At}\vec{u}(0), in so far as all we need to do after that is understand exactly what it means to take the...

Homework Statement (Reduction of order) The function y1 = x-1/2cosx is one solution to the differential equation x2y" + xy' + (x2 - 1/4) = 0. Use the method of reduction of order to find another linearly independent solution. The Attempt at a Solution I divided x2 to both sides to get the...

Let ##f(x,y)## be a scalar function. Then $$\frac{∂f}{∂x} = \lim_{h \rightarrow 0} \frac{f(x+h,y)-f(x,y)}{h} = f_x (x,y)$$ and $$\frac{∂}{∂y} \left (\frac{∂f}{∂x} \right ) = \lim_{k \rightarrow 0} \frac{f_x(x,y+k)-f_x(x,y)}{k} = \lim_{k \rightarrow 0} \left ( \frac{ \displaystyle \lim_{h...

Homework Statement I've been stuck on this problem for three days now, and I have no clue how to solve it. Construct a linear differential equation of order 2, for which { y_1(x) = sin(x), y_2(x) = xsin(x)} is a set of fundamental solutions on I = (0,\pi) . Homework Equations Wronskian for...

Homework Statement Find DEQ, circuit for time t>0. Homework Equations Ic= CdVc/dt Vl=LdiL/dt The Attempt at a Solution At T=inf L Short , C Open IL(inf)=4mA, VL(inf)=0, Ic(inf)=0, Vc(inf)=0 T=0- All at 0 T=0+ L=Open C=Short IL(0+)=0, VL(0+)=0, Ic(0+)=4mA, Vc(0+)=0 20v=L diL/dt + Vc +...

Homework Statement Okay the problem is of a free swinging pendulum with dampening which is modeled using the following equation: Damping coefficient: c=1 s−1 Mass: m=1 kg Gravity: g=9.81 ms−1 Link length: l=0.5 m We know θ(0)=90° and θ′(0)=0, solve this equation from t = 0 to t = 10...

Homework Statement [/B] I'm trying to 'solve' two coupled second order ODE's with the intent of putting them in state space. My specific problem is more complex and includes additional equations which are irrelevant. Essentially I can solve the problem if I know the solution to this. x1 and...

Homework Statement I am attempting to understand this example shown below: Homework Equations During stead state DC, the capacitor is an open circuit and the inductor is short circuited. The Attempt at a Solution [/B] The questions I have are really related to the concepts as I don't...

I don't know if this is a silly question? Am I missing simple math? How does a wave depending on amplitude and frequency make it's equation a second order differential equation?

how do you solve this equation? y´´ + k/(y^2) = 0 ? I got it from applying Newton's 2nd law of motion to an object falling from space to Earth only affected by gravitational force. Thank you!

Homework Statement Well I am looking for the particular integral of: d2y/dt2 + 4y = 5sin2t The attempt at a solution As f(t) = 5sin2t, the particular integral yPI should look like: yPI = Acos2t + Bsin2t dyPI/dt = -2Asin2t + 2Bcos2t d2yPI/dt2 = -4Acos2t - 4Bsin2t Subbing into the differential...

Hi guys, after hours of searching internet I couldn't find much real-life examples of second order nonlinear dynamic systems (only tons of tons of equation and system theory... got totally frustrated). They will serve as a base process for modeling controllers. So far I found propeller pendulum...

Homework Statement Regarding the case where the auxillary (characteristic) equation has complex roots, we solve the quadratic in the usual way using i to get the general solution y(x) = e^{\alpha x}\left(C_1 \cos{\beta x} + i C_2 \sin{\beta x}\right) And the textbook shows y(x) = e^{\alpha...