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 testing, A scientist calculates the temperature of melting plati...

A scientist calculates the temperature of melting platinum using a new type of thermometer. The temperature of the metal is called to be exactly 1768.3 centigrade. The measurements

Use lagrange interpolation to estimate function, Use Lagrange interpolation...

Use Lagrange interpolation to estimate f(3), given that f(1) = 1, f(4) = -3, f(2) = 0 and f(-1) = 3.

Math models, As an engineering student, the ministry of energy and minerals...

As an engineering student, the ministry of energy and minerals has tasked you to help them model equation(s) that can estimate the amount of crude oil in a reservoir. The governmen

Partial Differentiation, if the sides of a triangle ABC vary in such a way ...

if the sides of a triangle ABC vary in such a way that it''s circum-radius remains constant. prove that, da/cos A+db/cos B+dc/cos C =0

Simlple annuities and its application, analyn bought a dining set.She paid ...

analyn bought a dining set.She paid 2500 as a downpayment and promised to pay 800 @ the end of each month for year.What s the cash eqivalent of the set if the interest rate is 10%

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

Calculate principal value of the root, Compute the (real and imaginary part...

Compute the (real and imaginary parts of the) principal value of the eighth root of (a + ib) to 3 decimal places (accurate to 10 -3 ). Call the real part "m 7 ", and the imagina

Notice at the gym, You notice at the gym that it appears more women tend to...

You notice at the gym that it appears more women tend to work out together, whereas more men tend to work out alone.  To examine whether this difference is significant, you collect

Numerical integration, There are many situations which call for the replace...

There are many situations which call for the replacement of an integral by a sum, or vice versa. In the former case the highest accuracy is sometimes required. This means that in t

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