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Q: Why do you study about linear system while you are surrounded by nonlinear systems?

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We study the nonlinear systems to understand the behavior of some circuit elements in the transient state.

The amplifier is supposed to be an electronic circuit. Electronic circuits are nonlinear circuits, which may be modeled in the time domain by means of nonlinear differential equations and nonlinear algebraic equations. The kernel of the solution of the nonlinear equations is the solution of a linear equation system i.e. the nonlinear components and couplings are approximated with linear relations valid for small signals. Iterations are performed until the laws of Kirchhoff are fulfilled. The instant set of linear equations is the small signal model for the amplifier. If the amplifier is excited with a dc power source it assumes an active state called the bias point or quiescent point. If the relation between the input and the output signals of the amplifier is measured to be (almost) linear in the bias point then we assume a small signal amplifier with time independent bias point else we assume a large signal amplifier.

Any system that obeys the superposition theorem is, by definition, a linear system. So a non-linear system is one that does not obey the superposition theorem.

a nonlinear electrical load, like a battery charger or water heater when present in a power system produces harmonics or rather distortions which leads to improper proportionality of voltage to current. so that's an electrical load

It's a dynamical system that allows to reconstruct state vector of a nonlinear system using observation of the system output. See the Wikipedia article "State Observers".

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We study the nonlinear systems to understand the behavior of some circuit elements in the transient state.

Wilson J. Rugh has written: 'Nonlinear system theory' -- subject(s): System analysis, Nonlinear theories 'Linear system theory' -- subject(s): Control theory, Linear systems

Linear system follows principal of superposition and homogeneity and Non linear system does not follow the same.

Yes

linear system is like a chemistry equation or math equation where on both sides it must balance. Nonlinear is a math equation or physics that does not appear to have a direct answer just like chaos theory. lulu254ever

Iasson Karafyllis has written: 'Stability and stabilization of nonlinear systems' -- subject(s): Stability, Nonlinear systems, Mathematical Economics, Engineering, System theory

In general all systems are nonlinear but we simplify this nonlinear vibration to linear ones so that we can get approximate results. Approximate results are still good results in many cases. For example when you analyze the vibrations of the simple pendulum for small vibrations you don't need to include aerodynamic drag which is a nonlinear in its nature. By neglecting the nonlinear parts we can derive the second order differential equations which describes the motion of the system in this case gives linear vibration of simple pendulum. Another good example would be an examination of system which consists of block of mass m, spring with stiffness k and viscous damper with damping coefficient c and let's say that the block of mass m is in contact with the surface. Now the spring stiffness and the viscous damping are in reality nonlinear but for small vibration we assume they are linear. The bloc of mass m is in contact with the surface so that means that between the block and the surface is a friction. So if we analyze this system with nonlinear terms we would need to include the nonlinear stiffness, nonlinear damping coefficient and nonlinear friction. These would result in the time consuming calculation and in the end the results would little more precise than the approximation. In nonlinear analysis we attack the differential equation which describes the motion of nonlinear system with small parameter and with this we expand the solution. This method is called perturbation method. To solve nonlinear systems you need to use specific perturbation method and these methods are: Straightforward expansion, domain perturbation, multiple scale analysis etc. For more information check my site Linear Vibration.

In general, a system of non-linear equations cannot be solved by substitutions.

Aubrey M. Bush has written: 'Some techniques for the synthesis of nonlinear systems' -- subject(s): Discrete-time systems, Nonlinear theories, System analysis

J. K. Aggarwal has written: 'Notes on nonlinear systems' -- subject(s): Nonlinear theories, System analysis

They had the writing system, Linear A.

E. A. Grebenikov has written: 'Constructive methods in the analysis of nonlinear systems' -- subject(s): Asymptotic theory, Differential equations, Nonlinear, Iterative methods (Mathematics), Nonlinear Differential equations, System analysis

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