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A system with transfer function G(s) = ((s² + 9)(s + 2))/((s + 1)(s + 3)(s + 4)) is excited by sin(ωt). The steady-state output of the system is zero at

1. ω = 1 rad/s
2. ω = 2 rad/s
3. ω = 3 rad/s
4. ω = 4 rad/s

Correct answer: ω = 3 rad/s

Solution

The steady-state output of a system excited by a sinusoidal input is zero when the frequency of the input matches the natural frequency of the system's poles. In this case, the transfer function has a zero at ω = 3 rad/s, which leads to a cancellation of the output, resulting in a steady-state output of zero.

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