Unformatted text preview: 3 2 3 3 cos 2 t Ae t φ + is indicated. As such 2 the characteristic time, 3 = and 3 3 the damped natural frequency, 2 d = are indicated. Alternatively one could realize that 2 3 9 s s + + = is of the form 2 2 2 n n s s ςω + + = . Equating the last terms in the two expressions gives the undamped natural frequency, 3 n = while equating the middle terms gives 2 3 n = . Note that 2 2/ n = and thus, upon substitution 2 the characteristic time, 3 = could be found using this alternative procedure. Rearranging terms and substituting gives, 3 3 2 2 3 n = = i . Thus 1 the percent critical damping is, 2 = . Utilizing this latter information and the expression 2 1 d n =also leads to 3 3 the damped natural frequency, 2 d = ....
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 Spring '08
 Perreira
 damped natural frequency

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