832_Dynamics 11ed Manual

832_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Engineering Mechanics - Dynamics Chapter 22 yA e bt sin ω d t φ + () = A 0.0702 m = b 3.57 rad s = d 8.54 rad s = 0.00 rad = Problem 22-62 The damping factor C/C c , may be determined experimentally by measuring the successive amplitudes of vibrating motion of a system. If two of these maximum displacements can be approximated by x 1 and x 2 , as shown in Fig. 22-17, show that the ratio ln ( x 1 / x 2 ) = 2 π ( C / C c ) / ( 1 ( C / C e ) 2 ) 1/2 . The quantity ln( x 1 / x 2 ) is called the logarithmic decrement. Solution: xD e C 2 m t sin d t + () = x max De C 2 m t = x 1 De C 2 m t 1
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