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

Fourier Series, A function f(t) is defined as f(t) = p - t for 0 Write do...

A function f(t) is defined as f(t) = p - t for 0 Write down the even extension of f(t) for -p Determine the Fourier cosine series, and hence, calculate the Fourier series approx

Linear Programming, A company manufactures an assembly consisting of a fram...

A company manufactures an assembly consisting of a frame, a shaft, and a ball bearing. The company manufactures the shafts and frames but purchases the ball bearings from a ball be

Fuel tank, in the diagram shown below, the fuel tank which is of uniform cr...

in the diagram shown below, the fuel tank which is of uniform cross section and of length 8m is position so that the rear of the tank is 19 metres from the datum. the mass of the f

Control theory., Hi I have just received a math assignment and was wonder...

Hi I have just received a math assignment and was wondering if you can take a look at it and tell me if you can be finished before the 12th of february and what the cost will be.

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

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

definition of trigonometric function #Minimum 100 words accepted#

A cosmetic store offer , A cosmetic store offer at RM245 for a package, con...

A cosmetic store offer at RM245 for a package, consisting of a foundation, a compact powder and a lipstick, which is saving of 15% on the cost of buying the units indiviually. If b

Laplace transform, basic properties on the inverse of laplace transform

basic properties on the inverse of laplace transform

Series and sequence, #how do you estimate the sum a limit using intrgral te...

#how do you estimate the sum a limit using intrgral test

State the linear regression equation, An auto manufacturing company wanted ...

An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars

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