# What is Second order system: Definition and 17 Discussions

In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory.
First-order logic quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, also quantifies over relations. For example, the second-order sentence

P

x
(
P
x

¬
P
x
)

{\displaystyle \forall P\,\forall x(Px\lor \neg Px)}
says that for every formula P, and every individual x, either Px is true or not(Px) is true (this is the law of excluded middle). Second-order logic also includes quantification over sets, functions, and other variables as explained in the section Syntax and fragments. Both first-order and second-order logic use the idea of a domain of discourse (often called simply the "domain" or the "universe"). The domain is a set over which individual elements may be quantified.

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1. ### Find the resistive constant in a critically damped system

Homework Statement This problem is taken from Problem 2.3, Introduction to Vibration and Waves, by H.J. Pain and P. Rankin: A critically mechanical system consisting of a pan hanging from a spring with a damping. What is the value of damping force r if a mass extends the spring by 10cm without...
2. ### I Repeatability of necessity: number restrictions?

The necessity quantifier (aka Provability quantifier, or ~◊~, or Belief, or... instead of the usual square I will be lazy and call it "N") is often allowed to be repeated as many (finite) times as one wishes, so NNNNNNψ is OK. Is it possible to somehow include into the axioms some restriction on...
3. ### Calculating Contact Time and Damping Coefficient for a Second Order System

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

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...
5. ### A Normalization and Scaling with Matrices

Hey everyone, I understand how to normalize a second order system, but I wanted to know if the same steps are taken when the parameters of the system are not scalar but matrices. For example where the parameter phi, and gamma are both 3x3 matrices and X is a 3x1 vector. From what I've see...
6. ### Modelling: Second Order System

I have attached an image of a question I am trying to do, I want to find the differential equations that describe the second order system in the image. I know for a spring, potential energy = 1/2.K.x (where k is the spring constant, and x is the distance the spring is stretched). I know that...
7. ### Second order system of odes with variable coefficients

Hi, I have looked everywhere. Can someone please point me in the right direction for solving a system of ODEs with variable coefficients? I managed to solve such system with constant coefficients.
8. ### Maximum amplitude of second order system

See attached for the problem and attemped solution, its is not an applied problem, just a theoretical problem.
9. ### Midpoint Euler method, second order system

Hello I need to plot this simple system: x'' = -x using midpoint Euler. u1 = -x , u2 = -x' u1' = u2 u2' = -x u1(n+1) = u1(n) + h*? u2(n+1) = u2(n) + h*f((1/2)*(u1(n) + u1(n+1)) We don't know u1(n+1). I tried approximating it with u1(n+1) = u1(n) + h*u2(n) u2(1+i) =...
10. ### Second order system rise time question

Homework Statement The question is such : System is modeled as : y''+2y'+4y=u(t) find the time at which the system goes up 75,90,95 % of its final value.Homework Equations The Attempt at a Solution I have no idea how to touch that,I tried to find the source of the regular rise time (from 10...
11. ### Under-damped second order system - CONTROL

hey all, i'm stuck with the following designing problem (Control course) : Homework Statement given the location of the poles , find rise time , peak time, percentage maximum overshot and settling time for each pole. pole are: 1 . pole at θ = 70 , ωn = 1 2. pole at θ = 70 , ωn = 3...
12. ### Drawing the step response of a second order system

Homework Statement I have to draw the step response of the following two systems. G1 = (4+3s)/(s^2+4s+4) G2 = 3/(s^2+4s+4) So I started to draw the step response of the second system first. It has to be in the funky standard form: \frac{ω2}{s2 + 2ζωs + ω2} EDIT: Seems like the above doesn't...
13. ### Conditions of Stability for second order system

Homework Statement Consider the transfer function H(s)=\cfrac{1}{a_{2}s^{2}+a_{1}s+a_{0}} where real-valued coefficients a_{2},a_{1}, a_{0} are arbitrary except that a_{2} is nonzero. Verify that the system is stable iff the coefficients a_{2},a_{1}, a_{0} have the same sign. Homework...
14. ### Derivation of second order system transfer function

Hi, I am trying to derive the general transfer function for a second order dynamic system, shown below: \frac{Y(s)}{X(s)}=\frac{K\omega_n^2}{s^2+2\zeta\omega_ns+\omega_n^2} In order to do this I am considering a mass-spring-damper system, with an input force of f(t) that satisfies the...
15. ### Methods for Solving Non-Linear Second Order Systems of Differential Equations

Hi, could anyone tell me what methods I would need to solve this system: y\frac{d^2 y}{d\lambda^2}+\left(\frac{dx}{d\lambda}\right)^2-\left(\frac{dy}{d\lambda}\right)^2=0 \frac{y}{2}\frac{d^2x}{d \lambda ^2}-\left(\frac{dx}{d\lambda}\right)\left(\frac{dy}{d\lambda}\right)=0 I...
16. ### Bode Phase plot of a second order system

Hey guys. I need to know how to draw a Phase Bode plot of a Second order system. I understand and can draw the Gain(Magnitude) Bode plot, but I can't seem to get the grip of the Phase one. As far as I know there is an asymptote at 0^{o} at low frequencies and an asymptote at 180^{o} at...
17. ### MATLAB Second order system of differential equations in Matlab

Hi every one ! I am a final year Engineering student of IIT Madras, India. I am doing a project(finite element analysis of a structure) which requires the solution of a system of second order differential equations. equation looks like below: [M][U"]+K[U]=[F(t)] M : Mass Matrix of size...