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

Expression to be programmed in matlab, can you help be please to program a ...

can you help be please to program a complex expression in matlab using monte carlo solution

Geometric construction of numerical integration, The integral has a...

The integral has an exact answer, viz., sinc(pfT). As T®¥ the sinc function tends to zero. Divide the region from -T/2 to T/2 into N equal parts and sum the rectangles on b

Derivatives, At 8am particle A is at point (0,0) and moves horizontally to ...

At 8am particle A is at point (0,0) and moves horizontally to the right with constant velocity of 60km/hr. At the same time particle B is at the point (0, A+B+C+5) and moves horiz

Harmonic function, Let z 0 = a + ic, z 1 = b + id, z 2 = -id, and z =...

Let z 0 = a + ic, z 1 = b + id, z 2 = -id, and z = [z 0 + z 1 ]. Let z 0 be the apex of the wedge with one ray passing through z 1 and the other passing through z 2 , and

Explain how conduction takes place in conductors, With the help of energy b...

With the help of energy bands explain how conduction takes place in conductors. On the basis of energy band materials are categorized as conductor is given below: Conducto

Compute the linear arc distance, Question Assume the earth is a sphere ...

Question Assume the earth is a sphere with a radius of 6,371,000.000 meters. Three points are defined by their latitude and longitude. Point Latitude (N) Longitude (W) A

Some children are afraid of snakes, change each of the following propositio...

change each of the following propositions into symbolic form. De ne the universe of discourse and the predicates you use. (i) Some children are afraid of snakes. (ii) All com

Divison, What is the characteristics of divison

What is the characteristics of divison

Determine the missing entries, Determine the missing entries in the followi...

Determine the missing entries in the following divided difference table and use the result to estimate f(1/2).

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