# barcode generator vb.net source code VIBRATION AND CONTROL OF VIBRATION 31.2 in Software Creator EAN 13 in Software VIBRATION AND CONTROL OF VIBRATION 31.2

VIBRATION AND CONTROL OF VIBRATION 31.2
Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.
EAN-13 Supplement 5 Creation In None
Using Barcode drawer for Software Control to generate, create EAN-13 image in Software applications.
EAN / UCC - 13 Reader In None
Using Barcode decoder for Software Control to read, scan read, scan image in Software applications.
Generate GTIN - 13 In C#.NET
Using Barcode generator for .NET framework Control to generate, create European Article Number 13 image in .NET framework applications.
FIGURE 31.1 Representation of a single-degreeof-freedom system.
Painting EAN 13 In .NET
Using Barcode printer for ASP.NET Control to generate, create EAN13 image in ASP.NET applications.
Make EAN13 In Visual Studio .NET
Using Barcode printer for Visual Studio .NET Control to generate, create EAN / UCC - 13 image in .NET applications.
ficient of viscous damping c is the force provided by the damper opposing the motion per unit velocity. If the mass is given an initial displacement, it will start vibrating about its equilibrium position. The equation of motion is given by m + cx + kx = 0 x (31.1)
Drawing UPC - 13 In Visual Basic .NET
Using Barcode generator for Visual Studio .NET Control to generate, create GS1 - 13 image in Visual Studio .NET applications.
EAN13 Encoder In None
Using Barcode generator for Software Control to generate, create EAN / UCC - 13 image in Software applications.
where x is measured from the equilibrium position and dots above variables represent differentiation with respect to time. By substituting a solution of the form x = est into Eq. (31.1), the characteristic equation is obtained: ms 2 + cs + k = 0 The two roots of the characteristic equation are s = n i n(1 2)1/2 where n = (k/m)1/2 is undamped natural frequency = c/cc is damping ratio cc = 2m n is critical damping coefficient i= 1 (31.3) (31.2)
Barcode Creator In None
Using Barcode drawer for Software Control to generate, create barcode image in Software applications.
Data Matrix ECC200 Printer In None
Using Barcode maker for Software Control to generate, create ECC200 image in Software applications.
Depending on the value of , four cases arise. Undamped System (z = 0). In this case, the two roots of the characteristic equation are s = i n = i(k/m)1/2 and the corresponding solution is x = A cos nt + B sin nt (31.5) (31.4)
Making ANSI/AIM Code 128 In None
Using Barcode generation for Software Control to generate, create ANSI/AIM Code 128 image in Software applications.
Encode UPC-A Supplement 5 In None
Using Barcode maker for Software Control to generate, create UPC Code image in Software applications.
where A and B are arbitrary constants depending on the initial conditions of the motion. If the initial displacement is x0 and the initial velocity is v0, by substituting these values in Eq. (31.5) it is possible to solve for constants A and B. Accordingly, the solution is
Creating Identcode In None
Using Barcode maker for Software Control to generate, create Identcode image in Software applications.
Barcode Printer In None
Using Barcode drawer for Microsoft Word Control to generate, create barcode image in Microsoft Word applications.
GS1 128 Scanner In Visual Basic .NET
Using Barcode reader for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications.
Generate EAN13 In Java
Using Barcode generator for Android Control to generate, create EAN13 image in Android applications.
VIBRATION AND CONTROL OF VIBRATION 31.3
EAN 13 Drawer In C#.NET
Using Barcode generation for .NET Control to generate, create European Article Number 13 image in Visual Studio .NET applications.
Bar Code Encoder In C#.NET
Using Barcode generator for Visual Studio .NET Control to generate, create bar code image in Visual Studio .NET applications.
VIBRATION AND CONTROL OF VIBRATION
Universal Product Code Version A Reader In Java
Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications.
GTIN - 12 Creation In Java
Using Barcode drawer for Android Control to generate, create UPC A image in Android applications.
x = x0 cos nt +
v0 sin nt n
(31.6)
Here, n is the natural frequency of the system in radians per second (rad/s), which is the frequency at which the system executes free vibrations. The natural frequency is fn = n 2 (31.7)
where fn is in cycles per second, or hertz (Hz). The period for one oscillation is = 1 2 = fn n (31.8)
The solution given in Eq. (31.6) can also be expressed in the form x = X cos ( n ) where X = x2 + 0 v0 n
2 1/2
(31.9)
= tan 1
v0 n x0
(31.10)
The motion is harmonic with a phase angle as given in Eq. (31.9) and is shown graphically in Fig. 31.4. Underdamped System (0 < z < 1). When the system damping is less than the critical damping, the solution is x = [exp( nt)] (A cos dt + B sin dt) where d = n(1 2)1/2 (31.12) (31.11)
is the damped natural frequency and A and B are arbitrary constants to be determined from the initial conditions. For an initial amplitude of x0 and initial velocity v0, x = [exp ( nt)] x0 cos dt + which can be written in the form x = [exp ( nt)] X cos ( dt ) X = x2 + 0 and = tan 1 n x 0 + v0 d n x 0 + v0 d
2 1/2
nx0 + v0 sin dt d
(31.13)
(31.14)
An underdamped system will execute exponentially decaying oscillations, as shown graphically in Fig. 31.2.