Question 1: (2 marks) Find the zero-input response yz(t) for a linear time-invariant (LTI) system described by the following differential equation: j(t) + 5y(t) + 6y(t) = f(t) + 2x(t) with the initial conditions yz (0) = 0 and jz (0) = 10. Question 2: (4 marks) The impulse response of an LTI system is given by: h(t) = 3e?’u(t) Find the zero-state response yzs (t) of the system for each the following input signals using convolution with direct integration. (a) x;(t) = -28(t) + 2e-fu(t) (b) x2(t) = e-fu(t-1)
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