Forced - damped vibrations, Mathematics

Assignment Help:

It is the full blown case where we consider every final possible force which can act on the system. The differential equation in this case,

Mu'' + γu'  + ku = F( t)

The displacement function here will be

u(t) = uc(t) + UP(t)

Here the complementary solution will be the solution to the free, damped case and the exact solution will be found using undetermined coefficients or variation of parameter that ever is most convenient to utilize.

There are a couple of things to see now about this case. First, from our work back into the free, damped case we identify that the complementary solution will come to zero as t increases.

Due to this the complementary solution is often termed as the transient solution in this case. Also, due to this behavior the displacement will start to look more and more like the exact solution as t raises and so the particular solution is frequently termed as the steady state solution or forced response.


Related Discussions:- Forced - damped vibrations

Explain polynomials, P OLYNOMIALS : It is  not  once  nor  twice  b...

P OLYNOMIALS : It is  not  once  nor  twice  but  times  without  number  that the  same ideas make  their  appearance in the  world. 1.  Find the value for K for which

Evaluating a function, Evaluating a Function You evaluate a function by...

Evaluating a Function You evaluate a function by "plugging in a number". For example, to evaluate the function f(x) = 3x 2 + x -5 at x = 10, you plug in a 10 everywhere you

Integration and differentiation, Integration and Differentiation Diffe...

Integration and Differentiation Differentiation deals along with the determination of the rates of change of business activities or merely the process of finding the derivativ

Find out a particular solution to equation, Example: Find out a particular...

Example: Find out a particular solution to y'' - 4y' - 12 y = 3e 5t Solution The point here is to get a particular solution, though the first thing that we're going to

Determine the number of combinations, 3 items x, y and z will have 6 differ...

3 items x, y and z will have 6 different permutations however only one combination. The given formular is generally used to determine the number of combinations in a described situ

Probability - Compound Events, David wants to rent a movie. He wants to wat...

David wants to rent a movie. He wants to watch either a comedy or a drama. The movie rental store has 18 comedies and dramas available for rent. Seven of the movies are comedies, a

One-to-one function, One-to-one function: A function is called one-to-one ...

One-to-one function: A function is called one-to-one if not any two values of x produce the same y.  Mathematically specking, this is the same as saying,  f ( x 1 ) ≠ f ( x 2

Demerits and merit-the median, The median Merits i.  This shows t...

The median Merits i.  This shows the centre of a described set of data ii.  Knowledge of the determination of the median may be extended to find out the quartiles i

Prove that op=2ap, Two tangents PA and PB are drawn to the circle with cent...

Two tangents PA and PB are drawn to the circle with center O, such that ∠APB=120 o . Prove that OP=2AP. Ans:    Given : - ∠APB = 120o Construction : -Join OP To prove : -

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