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rotating imbalance. If the natural frequency of the system coincides with the frequency of rotation of the machine imbalance, it will result in severe vibrations of the machine and the support structure. Consider a machine of mass M supported as shown in Fig. 31.14. Let the imbalance be a mass m with an eccentricity e and rotating with a frequency . Consider the motion x of the mass M m, with xm as the motion of the unbalanced mass m relative to the machine mass M. The equation of motion is (M m) + m( + m) + cx + kx = 0 x x x The motion of the unbalanced mass relative to the machine is xm = e sin t Substitution in Eq. (31.40) leads to M + cx + kx = me 2 sin t x (31.42) (31.41) (31.40)

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-(void)buildVertexArrays { vertexIndex = 0; for (BBParticle * particle in childrenParticles) { . . if (animateColor) { [self addColorsR:particle.r g:particle.g b:particle.b a:particle.a vertexes:6]; } // for each particle, need 2 triangles, so 6 verts // first triangle of the quad. Need to load them in clockwise // order since our models are in that order [self addVertex:(particle.position.x - particle.size) y:(particle.position.y + particle.size) u:minU v:minV]; . . .

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There are not necessarily transitions in the data; for example, the ASCII null character is all zeros, so the start bit plus the 8 zero bits form one long pulse 9 bits long with no transitions: _____- - - - - -________ S00000000s ___ ____ ___-_____________ S11111111s ___ _____________ Transmission of ASCII null Start and data bits are 0s IrDA version, 9 short light pulses Transmission of ASCII $ff Data and stop bits are 1s IrDA version, 1 short light pulse.

This equation is similar to Eq. (31.25), where the force amplitude F0 is replaced by me 2. Hence, the steady-state solution of Eq. (31.42) is similar in form to Eq. (31.27) and is given nondimensionally as ( / n)2 sin ( t ) x M = [(1 2/ 2 )2 + (2 / n)2]1/2 e m n where tan = 2 / n 1 2/ 2 n (31.44) (31.43)

Note that since the excitation is proportional to 2, the response has an 2 term in the numerator and resembles the acceleration response of a system subjected to a force of constant magnitude, given by Eq. (31.35). The complete solution consists of the complementary part of the solution and is

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

x = exp nt {A exp [( 2 1)1/2 nt] + B exp [ ( 2 1)1/2 nt]} + me( / n)2 sin ( t ) M[(1 2/ 2 )2 + (2 / n)2]1/2 n (31.45)

It is fairly important that you build the color array before you start adding vertexes. Since you are setting the same color to each vertex, you can do it all at once, but the addVertex method increments the vertexIndex, so if you do not do the colors first, you will lose your place. As for the actual add colors method, it is pretty straightforward:

The IrDA receive circuitry must be able to detect the short pulses of light and stretch them to fill the standard bit width at the current baud rate for input to standard RS-232 serial ports. The above describes what is called the physical layer of IrDA. There are other layers that implement protocols for such things as sending packets of error-free data and for automatic negotiation of baud rate. We will not discuss these other layers in this project. The STAMP s limited brain would have trouble implementing those protocols. We are dealing here just with the physical layer, where IrDA is simply a wireless RS-232 substitute. The link must be tight to avoid errors, or you must implement some ad hoc error checking in software at both ends.

System Excited at the Foundation. When the system is excited at the foundation, as shown in Fig. 31.15, with a certain displacement u(t) = U0 sin t, the equation of motion can be written as m + c(x u ) + k(x u) = 0 x This equation can be written in the form m + cx + kx = cu0 cos t + ku0 sin t x = F0 sin ( t + ) (31.47) (31.46)

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

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