1. Find whether the system described by the following equation is linear, where x(t) is input and y(t) is output. dy · +

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1 Find Whether The System Described By The Following Equation Is Linear Where X T Is Input And Y T Is Output Dy 1 (78.95 KiB) Viewed 28 times

1. Find whether the system described by the following equation is linear, where x(t) is input and y(t) is output. dy · + 2y(t) = 4x(t) -3 dt Mathematically justify your answer. 2. Find whether the system described by the following equation is time-invariant, where x(t) is input and y(t) is output. y(t) = cos(x(t)) + x(t - 3) Mathematically justify your answer. 3. a) For the circuit shown in Fig. 3 prove that the system can be represented by the following differential equation, where x(t) is the input and y(t) is the output: (D2 + 4D + 2)y(t) = (D2 + 2)x(t) W 892 2 H + X(t) y (1) 1/4 FT b) Fig. 3 Find the zero-input response of the system described in question 4(a). The initial conditions are yo(0) = -1 and y(0) = -2.23. 4. = Find the impulse response of a system specified by the following equation, where x(t) is the input and y(t) is the output: (D2 + 3D)y(t) = 6x(t) [Hint: the initial conditions for calculating impulse response: ,(N-2) Yn (O) = yn (0) = y(0) = ... = yn (0) = 0 and yn 1] (N-1)(0)