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

Calculus, Ask questioA mass on a spring vibrates. Its position at time t fr...

Ask questioA mass on a spring vibrates. Its position at time t from its starting point is x(t) = 2 cos(t) e t Find the velocity and acceleration at time t. What is the behavior of

Draw parallel lines with slope, Draw parallel lines with slope +1.05; one p...

Draw parallel lines with slope +1.05; one passes through (0,a), and the other passes through (0,b). Suppose φ is a harmonic function between the two lines, with φ = 0 on the line t

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).

Dot plot graph, What does a dot plot graph look like with the measurements ...

What does a dot plot graph look like with the measurements 85.1 mm,85.0 mm,85.2 mm, and 85.1 mm

Process of repeated convolution, If x and y are two independent random vari...

If x and y are two independent random variables then their joint density function is given by The density function f z of the sum  of these two variables is given by the c

Value of n, Arrianna spended $5,500 at 7.5% p.a. compounded quarterly for '...

Arrianna spended $5,500 at 7.5% p.a. compounded quarterly for 'n' years. At the end of 'n' years, Arrianna got back $12,000. What is the value of n? (Approximate your answer in yea

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

., parabola

parabola

Provide a derivation, This is a pen and paper exercise, you are expected to...

This is a pen and paper exercise, you are expected to provide a detailed derivation. Follow the procedure outlined in the lectures for construction of a simple averaging by thr

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