(Solved): (g) Assume that the system with zero initial conditions is subject to an inpu ...

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(g) Assume that the system with zero initial conditions is subject to an input \( u(t)=0 \) for \( t<0, u(t)=\sin (3 t) \) for \( t \geq 0 \). Explain why the system output to such input approximates a sinusoidal function when \( t \) is large. [4 marks] (h) Using the Bode diagram of the system depicted in Fig. 2, describe the FIGURE 2: The Bode diagram for Question \( 1(\mathrm{~h}) \). response of the system to the input \( u(t)=0 \) for \( t<0, u(t)=\sin (4 t) \) for \( t \geq 0 \) when \( t \) is large.