First order system, Engineering Mathematics

Assignment Help:

As with the first order system, there is a general differential equation that governs the response of a second order system.  The equation is of the form:

1359_First order system.png

Where:

919_First order system1.png

So how is the second order differential equation for the spring mass damper generated?

Well, if an input is applied to the mass, the equation of motion for the system can be written as:

 

The general equation for a second order system can be manipulated to give the equation above and vice versa.

1836_First order system3.png

Performing the numerical integration for the second order system

The second order equation order is dealt with by rewriting the equation as pair of first order equations.  The numerical integration can be performed in a similar way to the first order system where:

 

1869_First order system4.png

Of course as all the hardware information is available or selected by the engineer, the value for (d2y/dz2)  can be calculated by manipulating the equation of motion.

498_First order system5.png


Related Discussions:- First order system

Chemistry, advantages of langmuir adsorption theory

advantages of langmuir adsorption theory

Set up a scatter diagram for speed, A research analyst for an oil company w...

A research analyst for an oil company wants to develop a model to predict miles per gallon based on highway speed. An experiment is designed in which a test car is driven at speeds

Temperature function, If a temperature function is given in the x,y plane b...

If a temperature function is given in the x,y plane by T(x,y) = x+y, what is the value, to 3 decimal places, of the corresponding temperature function T1(u,v) at the point (u,v) =

Permutation and combination, The number ways of choosing 2 boys and 2 girls...

The number ways of choosing 2 boys and 2 girls in a class for a game of mixed doubles is 1620. Then, what is the number of ways of choosing 2 students in the class?

Fuel tank, in the diagram shown below, the fuel tank which is of uniform cr...

in the diagram shown below, the fuel tank which is of uniform cross section and of length 8m is position so that the rear of the tank is 19 metres from the datum. the mass of the f

Evaluate the expression for various smoothers, Evaluate the expression belo...

Evaluate the expression below for various smoothers, plot and compare the results, making appropriate comments.

Polynomial approximation, how to program lagrange polynomial approximation ...

how to program lagrange polynomial approximation with MATLAB

Lean manufacturing, Ask quassignment writing estion #Minimum 100 words acce...

Ask quassignment writing estion #Minimum 100 words accepted#

Bad Illustration, There is an illustration of a diesel engine sixteen cylin...

There is an illustration of a diesel engine sixteen cylinder that is supposed to be four-cycle, however GM never made engines of that size that were not two-cycle. The four valves

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd