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# Real Functions in One Variable - Simple 2... - eBooks and textbooks from bookboon.com

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Nguyễn Gia Hào

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Find the roots of the characteristic polynomial and then the complete solution of the corresponding homogeneous equation. The characteristic equationR2+ 2R+ 2 = 0 has rootsR=−1±i, so it is a complete solution of the homogeneous equation.

## STUDY AT A TOP RANKED

Find the roots of the characteristic polynomial and apply the structure of the complete solution. Therefore, if ϕ0(t) is any particular solution, then the complete solution of the inhomogeneous differential equation is given by.

## 3 Other types of linear diﬀerential equations

It can be shown that two solutions found by two different methods differ only by a constant.

## 4 Mathematical models

This amplitude therefore depends on the frequency of the angle ω on the right-hand side of (24). Example 4.5 The figure shows a setup where a horizontal plate rotates at a constant angular velocity Ω. The constants k and mare remain unchanged in the following, and the movement of the mass depends only on the angular velocity Ω.

A disk rotating at angular velocity Ω with a particle fixed to a spring in a tube that is fixed to the disk. These are described on the axis oriented by x= 0 dhex= , where denotes the length of the axis. In fact, draw the cord between the particle and the rod point on the periphery.

Then this chord is clearly shorter than the length 1 of the rod, and in turn is also the hypotenuse of a right triangle, in which one of the shorter sides (given by the projection of the particle on the diameter) is 1. .

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