For the RL circuit shown above, assume that the component values are R = 10002 and...

  

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For the RL circuit shown above, assume that the component values are R = 10002 and L= 10H. Part A) Find the differential equation that relates the source voltage, x(), to the inductor voltage, y(). Write your differential equation in the form dy b₁+boy(1) = x(1) dt and provide the values of the constants bo. b as a 2-element row vector of the form b = [bo, bl. Note: Your differential equation should be scaled so that the coefficient of the x(t) term is 1. Part B) Treating this circuit as a system with an input, x(1), and an output, y(), find the impulse response of this system. Provide your answer as a function, h(r) of the scalar input variable t Part C) Find the output of this system if the input is x(1) = u(1). That is, find the step response of this system. Provide your answer as a function, y(t) of the scalar input variable r x(t) L R y(t) 1 For the RL circuit shown above, assume that the component values are R = 10002 and L= 10H. Part A) Find the differential equation that relates the source voltage, x(), to the inductor voltage, y(). Write your differential equation in the form dy b₁+boy(1) = x(1) dt and provide the values of the constants bo. b as a 2-element row vector of the form b = [bo, bl. Note: Your differential equation should be scaled so that the coefficient of the x(t) term is 1. Part B) Treating this circuit as a system with an input, x(1), and an output, y(), find the impulse response of this system. Provide your answer as a function, h(r) of the scalar input variable t Part C) Find the output of this system if the input is x(1) = u(1). That is, find the step response of this system. Provide your answer as a function, y(t) of the scalar input variable r x(t) L R y(t) 1