Consider the following transfer function:
$\frac{Y}{X} = \frac{A_0}{\omega_o^2 s^2 + 1} $
or something similar that is supposed to represent an undamped block on a spring. I encountered the following question about it which has me flummoxed:
Linear systems, when given a pure oscillating input, are supposed to produce an output signal that is also a pure oscillating output and at the same frequency. However, an oscillating input at resonance produces an output in the form $t \cos \omega_ot$. That signal is not a single frequency. What is going on? Is this still a linear system?