Unformatted text preview: ( t ) + c ˙ y ( t ) + ky ( t ) = klMg + meω 2 sin ωt and with y ( t ) = x ( t ) + lMg k one obtains the equation for x ( t ). The steadystate amplitude is then given by A = meω 2 r ( kMω 2 ) 2 + ( cω ) 2 which implies that 2 ζ A  ω = √ k m = lim ω →∞ A 4. In terms of the damping factor ζ and the ratio r between ω and R k/m , the steadystate amplitude is given by A = Y ± 1 + 4 r 2 ζ 2 1 + 4 r 2 ζ 2 + r 2 ( r 22) In particular, the term r 2 ( r 22 ) is positive for r > √ 2. 3. An approximate solution of period 2 π is here given by x ( t ) =1 . 57 cos t. 00677 cos3 t 1...
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 Spring '08
 Weaver
 Ratio, Period, Mechanical Science and Engineering, steadystate amplitude

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