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

Linear programming, A paper mill produces two grades of paper viz., X and Y...

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

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

Find the sum of the three coefficient polynomials, Find the quadratic that ...

Find the quadratic that interpolates f(x) = 2x 3 - x + 1 at the nodes x 0 = 0, x 1 = 2, x 2 = 3, a) by solving a set of three equations for the coefficients of p 2 (x) = a 2

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

Compute the real and imaginary parts, The data in this exam are a set of 6 ...

The data in this exam are a set of 6 integers a through f, based on your social security number. Write the LAST 6 digits of your social security or ID number in the spaces below, t

Fast fourier transform, From this point on it is assumed that any problem a...

From this point on it is assumed that any problem amenable to solution with the aid of the Discrete Fourier Transform (or DFT) will in fact be treated computationally with a fast r

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

Mann''s test for the weibull distribution, How do i perform mann''s test fo...

How do i perform mann''s test for the weibull distribution

Modelling equations , how to model equations to determine the amount of oil...

how to model equations to determine the amount of oil in a reservior

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