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

Pythagorean theorem, when one side of a triangle is 15cm and the bottom of ...

when one side of a triangle is 15cm and the bottom of the triangle is 12cm what would x be rounded to the nearest tenth?

Basic indefinite integrals- computing indefinite integrals, Basic indefinit...

Basic indefinite integrals The first integral which we'll look at is the integral of a power of x.                                ∫x n dx = (x n +1 / n + 1)+ c,          n

Find the 20th term of arithmetic progressions, Find the 20 th term from th...

Find the 20 th term from the end of the AP 3, 8, 13........253. Ans:    3, 8, 13 .............. 253 Last term = 253 a20 from end = l - (n-1)d 253 - ( 20-1) 5 253

Factoring, how are polynomials be factored/?

how are polynomials be factored/?

Evaluate following unit circle, Evaluate following sin 2 ?/3   and sin (-2 ...

Evaluate following sin 2 ?/3   and sin (-2 ?/3) Solution: The first evaluation in this part uses the angle 2 ?/3.  It is not on our unit circle above, though notice that  2 ?/

Parallel vectors - applications of scalar multiplication, Parallel Vectors ...

Parallel Vectors - Applications of Scalar Multiplication This is an idea that we will see fairly a bit over the next couple of sections.  Two vectors are parallel if they have

Algebra, please tell me what is algebra and how i can understand it

please tell me what is algebra and how i can understand it

Market testing, what are the dangers of not market testing a product

what are the dangers of not market testing a product

Finding length and height with volume and width?, I figured out the volume ...

I figured out the volume and the width, but I have no idea how to use that information to get the height and the length!

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