(adsbygoogle = window.adsbygoogle || []).push({}); Mistake 1.

In the lecture slides from my university it says that:

"The response of a stable first-order transfer function to a unit sine wave input is:"

[itex]Y(s)=\frac{1}{s+a}*\frac{\omega}{s^2+\omega^2}[/itex]

Isn't this missing an [itex]a[/itex] in the numerator since the standard form of a first order transfer function is:

[itex]H(s) = \frac{1}{\tau s +1} = \frac{a}{s+a}[/itex]

where [itex]\tau=1/a[/itex]

and the laplace transform of the sine wave input is:

[itex]\frac{\omega}{s^2+\omega^2}[/itex]

Mistake 2.

The lecture slides also say that:

"The response of a stable second-order transfer function to a unit sine wave input is:"

[itex]Y(s)=\frac{1}{s^2+2\zeta\omega_n+\omega_n^2}*\frac{\omega}{s^2+\omega^2}[/itex]

Similarly, isn't this missing an [itex]\omega_n^2[/itex] in the numerator as the standard form of a second order transfer function is:

[itex]H(s) = \frac{\omega_n^2}{s^2+2 \zeta \omega_n s + \omega_n^2}[/itex]

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# Is this equation from my lecture notes wrong? (RE: Transfer Functions)

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