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

Hypothesis of this statement , A) For a given integer n, if n   2 is divisi...

A) For a given integer n, if n   2 is divisible by 4, then n2   4 is divisible by 16. State the hypothesis of this sentence and the conclusion. Give a direct proof of the statement

Does the adverse reaction of nausea, The table summarizes results from a cl...

The table summarizes results from a clinical trial (based on data from Pfizer, Inc). Use a 0.05 significance level to test the claim that experiencing nausea is independent of whet

Time, Two boys A and B are at two diametrically opposite points on a circle...

Two boys A and B are at two diametrically opposite points on a circle. At one instant the two start running on the circle; A anticlockwise with constant speed v and B clockwise wit

Explain how conduction takes place in semiconductors, With the help of ener...

With the help of energy bands explain how conduction takes place in semiconductors. Semiconductors: Substances as carbon, germanium and silicon that electrical conductivity l

Profit per unit , A company's full profit per unit production is given by t...

A company's full profit per unit production is given by the function y = -5x 2 +17x-12  where x is the number of items produced (in hundreds) and the y is the profit per unit (in

#titlExample - Electronics application of 3×3 System of Ee.., #quExample - ...

#quExample - Electronics application of 3×3 System of Equations Find the electric currents shown by solving the matrix equation (obtained using Kirchhoff''s Law) arising from this

Numerical analysis, The system has a solution near (-0.5,-0.7). Set...

The system has a solution near (-0.5,-0.7). Set up the matrix equation Jδ = -f for Newton's method and then carry out one iteration, starting with x 0 = -0.5, y 0 = -0.7.

All.., Ask question #Minimum 100thank you words accepted#

Ask question #Minimum 100thank you words accepted#

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