822_Dynamics 11ed Manual

822_Dynamics 11ed Manual - Engineering Mechanics Dynamics...

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Engineering Mechanics - Dynamics Chapter 22 Solution: M y'' c y' + 3 ky + 0 = y'' c M y' + 3 k M y + 0 = ω n 3 k M = ζ c 2 M n = Since 0.65 = < 1 the system is underdamped b ζω n = d 1 2 n = yt () e b t A cos d t B sin d t + = Now find A and B from initial conditions. Guesses A 1m = B = Given 0 A = vA bB d + = A B Find AB , = e b t A cos d t B sin d t + = where b 7.50 rad s = d 8.87 rad s = A 0.0 mm = B 33.8 mm = Problem 22-49 The instrument is centered uniformly on a platform P , which in turn is supported by four springs, each spring having stiffness k . If the floor is subjected to a vibration
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