Consider a system S, with input u(t) and output y(t) whose behavior is modeled by the...

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Consider a system S, with input u(t) and output y(t) whose behavior is modeled by the following differential equation: ÿ(t) + 7y(t) + 10y(t) = 10u(t) (a) Find the impulse response (h(t)), step response (y₁ (t)) and transfer function of this system. (b) Determine the response of the system to the input shown in Fig. 1 in terms of y₁ (t). 2 0 u(t) C 10 15 Consider a system S, with input u(t) and output y(t) whose behavior is modeled by the following differential equation: ÿ(t) + 7y(t) + 10y(t) = 10u(t) (a) Find the impulse response (h(t)), step response (y₁ (t)) and transfer function of this system. (b) Determine the response of the system to the input shown in Fig. 1 in terms of y₁ (t). 2 0 u(t) C 10 15