Difference between revisions of "A typo in equation (6.24)."

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m (Typo in CDS110 problem 1(a). moved to A typo in equation (6.24).)
 
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The closed loop transfer function <math>G(s)\,</math> (which means <math>H_{yr}(s)\,</math>) should be <math>\frac{\omega_0^2}{s^2+2\zeta\omega_0s+\omega_0^2}\,</math>. The last term of the denominator is <math>\omega_0^2\,</math> rather than <math>\omega_0\,</math>, and the second term is missing an additional <math>s\,</math>.
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For <math>\zeta<1\,</math>, the corresponding equation should be:
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<math>y(t)=k\Big(1-e^{-\zeta\omega_0t}\cos{\omega_dt}-\frac{\zeta}{\sqrt{1-\zeta^2}}e^{-\zeta\omega_0t}\sin{\omega_dt}\Big)</math>.  
  
 
--Shuo
 
--Shuo

Latest revision as of 00:36, 23 November 2008

For \(\zeta<1\,\), the corresponding equation should be\[y(t)=k\Big(1-e^{-\zeta\omega_0t}\cos{\omega_dt}-\frac{\zeta}{\sqrt{1-\zeta^2}}e^{-\zeta\omega_0t}\sin{\omega_dt}\Big)\].

--Shuo