Page 542 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Answers to Selected Problems 529

3-25 k = 18.8 Ib/in. each spring
3-28 X = 0.01105 cm, Fj = 42.0 N
3-29 o) ^X= 3.166 cm/ s"
3-38 Cgq = 4D/7T(t)X
3-42 (a) 15.9 cps, (b) 7.45 cps
3-45 (a) 624.5 m.v., (b) 3.123 m.v.
3-48 E = 25.7 m.v./g

CHAPTER 4
f
4-5 X = “^[cos - 6 )) - cos o),j] t > in
100/.
X
20 .
4-10 z = —:r(l “ cos (o^t)------sin co^t
100 20

1 -
]f25 + +
^Jmgs/k
4-13 tan (o^t =
5 —m g/4k

4-14 X 12.08 in., t = 0.392 s
4-29 - = 1.65
g
4-30 y ,,, = 10.7g
4-31 x(t) = + sin ' 7 l - - C0Sft>„/|

y(0) V e
4-45 yit) = y(0)cos o)t + ' sin w t + — ( w t — sin w l ) — —^-d —cos w t )

CHAPTER 5
5-2 w \ = k / m , (A j/A j)] = 1
(ol = 3 k / m , ( A ,/A 2)2 = - 1
5-4 ojj = 0 .5 7 0 k /m , ( A ,/A 2>, = 3.43
ojj = 4.096A:/w, (A , 7 ^ 2)2 = -0.096
5-8 o)„ = 15.72 rad/s
5-10 0, + 2g//0, - g/102 = 0
0, + 02 + g//02 = 0
5-13 = 0.796y/T/ml, (A, 7^ 2)1 = 1-365
o>2 = \.538^T/ml, (A,7 ^2)2 = -0.366
5-15 w = y j H----^ (1 ± 1) , beat period = 53.02 s
-
ml^