Page 552 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Answers to Selected Problems 539
_ ^ f
13-35 y^ = ^ = 0.00438, a = 0.0662w
P[|y| > 0.132] = 2a = 4.6 percent
13-36 o- = 0.0039m, P[|y| > 0.012] = 0.3 percent

CHAPTER 14
2Tn 1 / EA

14-2 mx + -r^x 1 + ^ - I t = 0
2 r,,
ttvIp
14-3 nvc + -[(/? - x)' - ( h - JC,,)']
3(/j -Xn)
To = radius of circle at water line
p = wr/vol of water
14-8 V = 5 X = y = 0 for equilibrium

14-11 Shift origin of phase plane to tt in Fig. 14.4-2
14-13 Aj 2 = 3,4,
0.5 1
14.14 { ; ) = ■
1 1
14-25 y =
dx
14.27 f where S = { ^ y + - f - x ^
dx y \m^ o)lm
(ol= k/m
dx
T = o)„t, y =
dr
/ /•6(r de / r'ir/2 d e
14-30 T = 4 = 4
^ ^ y/2(cos 6 - cos 0 y^l - A^sin^i/)
0 0
where k = sin-^, sin -^ = /: sin (/>
14-34 o> s i/ 4- i 1 + ^ « 0

14-40 mx X, + | ^ ) x H 0 , T =T , + Kj-^

Second approximation

mx9 + ( + 3ax^X2 = 0, a = ^
V / 6
iiZ o 3 \ 3
m i- T -I- I + j + cos 2a)„/ Xt = 0