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which yields T = Icq c + m1 R tan f ( y q c2 + y q c ) y = R tan fq c = y q c y = R tan f Therefore, from Eqs (1217), (1218), and (1219) (q i - q c )ks + k f ( x - y) y - m1 y y q c2 = ( Ic + m1 y 2 )q c Summing forces on mass m2 at the follower top m2 x = k f ( y - x ) If there is no model mass m1 those terms in the equation will be eliminated 1244 Four-Degree-of-Freedom System Next, let us analyze a four-degree-of-freedom model with coupled elastic follower and elastic torsional and exural camshaft (Fig 1221) to further study the effects of exibility in the driveshaft on the vibratory response of the cam follower Figure 1222 shows the sketch of the system which has a closed-track cam-follower system Note in Figs 1221 and 1222 that the cam is located at the middle of the elastic shaft for convenient analysis However, it is an essence of good design not to locate the cam in the center of the shaft, permitting de ections in three directions The cam is usually located as close to a rigid bearing as possible, largely to eliminate the exural vibrational factors Also, a phenomenon exists in the closed-track system, see Wiederrich (1220) (1218) (1219)

.

(227) (228)

Now graph the function At t = 0, p = 45 as given in the problem As time goes on, the 144t term gets smaller and smaller and as t + m , p j 2 5 The line p = 2 5 is an asymptote The curve is shown in Fig 10-10

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1 A solid has base the unit circle in the x-y plane and vertical slices, parallel to the y-axis, which are discs with centers in the x-y plane and diameters extending across the base circle Calculate the volume of this solid 2 A solid has base a unit square with center at the origin and vertices on the x- and y- axes at the points ( 1, 0) and (0, 1) The vertical cross section of this solid, parallel to the y-axis, is an equilateral triangle What is the volume of this solid 3 Set up the integral to calculate the volume enclosed when the indicated curve over the indicated interval is rotated about the indicated line Do not evaluate the integral 2 x 4 x-axis (a) y = x 3 3 (b) y = x 1 x 8 y-axis 0 x 2 y = 1 (c) y = x 1/2 (d) y = x + 3 1 x 2 y=4 1/2 4 x 6 x = 1 (e) y = x (f) y = cos x 0 x /2 y=0 4 Set up the integral to evaluate the indicated surface area Do not evaluate (a) The area of the surface obtained when y = x 1/3 , 0 x 4, is rotated about the x-axis (b) The area of the surface obtained when y = x 1/5 , 1 x 3, is rotated about the y-axis (c) The area of the surface obtained when y = x 3 , 0 x 3, is rotated about the line y = 2 (d) The area of the surface obtained when y = cos x, 0 x /2, is rotated about the x-axis (e) The area of the surface obtained when y = x 1/3 , 1 x 4, is rotated about the line x = 2 (f) The area of the surface obtained when y = x 4 , 0 x 1, is rotated about the x-axis 5 A water tank has a submerged window that is in the shape of a circle of radius 3 feet The center of this circular window is 10 feet below the surface Set up, but do not calculate, the integral for the pressure on the lower half of this window---assuming that water weighs 624 pounds per cubic foot.

(229)

Jerk y''' =

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Transaction point Displacement, y Velocity, y' Acceleration y"

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