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

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

Mechanics, elongation of conical bar under its own weight is what fraction ...

elongation of conical bar under its own weight is what fraction of rectangular bar

Matrics, #find inversquestion..

#find inversquestion..

Find the controllability matrix, An open-loop control system has the follow...

An open-loop control system has the following state-space model: (a) Find characteristic equation of the open-loop control system model. (b) What is the characteristic e

Weighted aggregate , The data of the table below give details of the compon...

The data of the table below give details of the components, prices and standard quantities used in making a kind of chemical. Measure  the composite index with 2007 as base year us

I am looking for engineering math solution, HEllo, i am looking for math so...

HEllo, i am looking for math solutions online? Let me know how to get it?

Thermal stress, a restrained steel bar is heated from 20 degrees to 194 deg...

a restrained steel bar is heated from 20 degrees to 194 degrees and not permitted to expand. the bar is 10mm diameter, determine the thermal stress in the bar

Find the equilibrium points, Find the equilibrium points (real and imaginar...

Find the equilibrium points (real and imaginary parts, to 3 decimal places) if unit positive line charges are placed at a+ic, b+id, and -3-2i. Designate one of these numbers as "m

Database management system, outline the three schema database architecture ...

outline the three schema database architecture clearly explaining each level and how the user view the information

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