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

Some children are afraid of snakes, change each of the following propositio...

change each of the following propositions into symbolic form. De ne the universe of discourse and the predicates you use. (i) Some children are afraid of snakes. (ii) All com

Divison, What is the characteristics of divison

What is the characteristics of divison

Strength of materials, a wire of 3mm diameter and 5 m long has a load of 10...

a wire of 3mm diameter and 5 m long has a load of 100g suddenly applied to its ends. calculate stress and extension produced. also show that these are twice the static values

Produce a discrete time series, Produce a discrete time series y(t i ) by s...

Produce a discrete time series y(t i ) by super positioning 5 cosinusoidal components, for your own choice of the amplitudes (a j ) and frequencies (f j ). Add some Gaus

Linear programming, A paper mill produces two grades of paper viz., X and Y...

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

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

definition of trigonometric function #Minimum 100 words accepted#

Draw concentric circles, Draw concentric circles of radii a and b, each cen...

Draw concentric circles of radii a and b, each centered at z=id (on the imaginary axis). Suppose φ(x,y) is a harmonic function inside the washer defined by these circles. The circl

Perform arithmetic computation, a.) Give a short sequence of machine instru...

a.) Give a short sequence of machine instructions for the task " Add the contents of memory location A to those of memory location B, and place the answer in location C ". You have

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

Work laws for closed systems, In closed system 0.3kg of gas at 373K is expa...

In closed system 0.3kg of gas at 373K is expanded isothermally and reversibly from 1 mpa pressure to 200 kp. Given that cv= 718 j/kg k and R= 287 j/kgk.

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