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?