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

I need a quote, i need a quote in analytical methods for engineers (Algebr...

i need a quote in analytical methods for engineers (Algebraic methods)

Solve the following logarithmic equations, 1. Joe and Sam each invested $20...

1. Joe and Sam each invested $20,000 in the stock market. Joe's investment increased in value by 5% per year for 10 years. Sam's investment decreased in value by 5% for 5 years and

Sinusoidal trigonometrical function, The displacement x meters of a mass fr...

The displacement x meters of a mass from a fixed point about which it is oscillating is given by x=2.3cos?10pt+4.2sin?10pt where t is the time in seconds Express the displaceme

Maths, How to solve the problems

How to solve the problems

Accurately measure the fluid level, You are working as an engineer on a pro...

You are working as an engineer on a project that involved being able to accurately measure the fluid level change in a large outdoor holding tank. The fluid level rises and falls a

Trigonometric functions, definition of trigonometric function #Minimum 100...

definition of trigonometric function #Minimum 100 words accepted#

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

Dynamics, The acceleration of an oscillating particle is defined by the rel...

The acceleration of an oscillating particle is defined by the relation a = -kx Determine the value of k such that v = 15 in./s when x = 0 and x = 3 in. and v = 0, the speed of the

Define a mapping from the x-y plane, Define a mapping from the x,y plane to...

Define a mapping from the x,y plane to the u,v plane by u = 2x + y, v = -x +2y . If a temperature function is given in the x,y plane by T(x,y) = x+y, what is the value, to 3 de

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