Page one 1. you are given a first-cedier semsor with a time constant r. (9 points total)

a the input to this sensor is given by xt) st where "s" is the slope and it is a constant. l white an expression for the instantaneous sensor output error in steady state. (2 points) il write an expression for the time delay in the sensor output in steady state. (2 points)
b. the input to this sensor is given by xt) = xosin ot. the output magnitude and phase of the sensor will have a systematic error except for one particular (and not very practical! ) case. write the expression which defñnes this one particular case. (be specific). (2 points) %3d
c. the input to this sensor is a step input applied at time t 0. the value of this step function is given by xe for t> 0. the output of the sensor, y(t), at t 0 is given by 0. thus; y(t = 0) = 0. the error in the reading of the sensor is defined as; error in reading = e(t) = (true value of the measurand) - (reading of the sensor) ! 3! write the expression for e(t) for all t> 0. (3 points) are given a second-order sensor with damping coefficient uency on. and undamped na: input to this sensor is given by x(t) = xo°sin ot. select the appropriate variable = an expression which will define the region where the systematic error in the c itude of this second-order sensor is guaranteed to be very low. (2 points)