Q:

Response of a stable second-order transfer function to a unit sine wave input

In the lecture slides from my university it says that:
"The response of a stable second-order transfer function to a unit sine wave input is:"
$$Y(s)=\frac{1}{s^2+2\zeta\omega_n+\omega_n^2}*\frac{\omega}{s^2+\omega^2}$$
Isn't this missing an \$ω_n^2\$ in the numerator?  Since the standard form of a second order transfer function is:
$$H(s) = \frac{\omega_n^2}{s^2+2 \zeta \omega_n s + \omega_n^2}$$
and the laplace transform of the sine wave input is:
$$\frac{\omega}{s^2+\omega^2}$$
Is this a mistake in the lecture slides? 

A:

You are probably right, but it depends on how you define the transfer function.  The sine part is right, while as you can see your \$H(s)\$ is not adimensional, it's something like \$s^2\$, that is pretty strange for a transfer function[^seconds]. 
You are safe assuming that's a slide mistake.  For the future keep in mind that checking the measurement units is always a great idea. 
[^seconds]: the s is for seconds, not for the s variable.