5.2 A system with dynamics described by $$G(s) = \frac{X(s)}{F(s)} = \frac{0.25}{s^2 + 2s + 2}$$ is subjected to a sine wave input depicted graphically in the figure below. Input, f(t) -2 0 4 2 -4 0 1.5708 3.1416 4.7124 Time (s) Determine the expected steady-state output, $$x_{ss}(t)$$.
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The amplitude is 4, and the period is approximately 3.1416, which is $$\pi$$. Therefore, the frequency $$\omega$$ is given by: $$\omega = \frac{2\pi}{T} = \frac{2\pi}{\pi} = 2$$ Show more…
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