Simulating the second order system, Engineering Mathematics

Assignment Help:

First systems were described as systems that had one method of storing energy.  Second order systems; wait for it.... have two methods of storing energy.  Using a similar mechanical system to the first order case, the common spring mass damper system is a good example of a second order system.

The spring and the mass are both capable of storing energy whereas the damper can only dissipate energy.

866_Simulating the second order system.png

Consider the situation with the damper removed.  If a force is applied to push the mass down, then strain energy is stored in the spring.  As the mass is released, this energy is converted into kinetic energy in the mass as it starts to move.  This KE becomes potential energy as the mass gains height.  The potential energy then becomes kinetic energy which then becomes strain energy in the spring and so on.  The system oscillates as energy is transferred from the mass to the spring and back again.  In theory the system oscillates continuously.  In reality of course, the system loses its energy to the surrounding, there is resistance as the mass travels through the air and the spring generates heat and therefore the after a period of time the system does come to rest.  In many real world applications the spring mass is fitted with a damping device in order to control system behaviour and in most cases to "dampen out" oscillations.


Related Discussions:- Simulating the second order system

Dynamics, The acceleration of an oscillating particle is defined by the rel...

The acceleration of an oscillating particle is defined by the relation a = -kx Determine the value of k such that v = 15 in./s when x = 0 and x = 3 in. and v = 0, the speed of the

You are required to design an air-conditioner controller for, Below are the...

Below are the conditions specified by the institution: a) If the temperature sensor shows 30 degree Celsius or higher, the air-conditioner will be turned ON regardless of the othe

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

Divison, What is the characteristics of divison

What is the characteristics of divison

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).

Calculate the sequence from aitken’s method, Values from the iteration x = ...

Values from the iteration x = cos(x) are: x 0 = 0.8, x 1 = 0.696707, x 2 = 0.766959, x 3 = 0.720024, x 4 = 0.751790, x 5 = 0.730468. a) Calculate the sequence {y n } fr

Compounded monthly , Verify how long $400 must be left to store at 12 % p.a...

Verify how long $400 must be left to store at 12 % p.a. compounded monthly for it to amount to triple the soted value of another $400 deposited at the similar time at 8.8% p.a. com

Compute the real and imaginary parts, The data in this exam are a set of 6 ...

The data in this exam are a set of 6 integers a through f, based on your social security number. Write the LAST 6 digits of your social security or ID number in the spaces below, 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