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Frequency response based design: Lag Consider a unity feedback system with the plant Gp = 1 / ( (s+3) (s2 + 2s + 4) )  Here is some information from the Bode of Gp(s): At frequency ω = 0 rad/s magnitude is -21.6 dB  and phase is 0  degAt frequency ω = 2.24 rad/s magnitude is -24.7 dB   and phase is -140  degAt frequency ω = 7.85 rad/s magnitude is -54 dB   and phase is -234  degAt frequency ω = 69 rad/s magnitude is -110 dB   and phase is -266  deg Compute the gain K that will yield overshoot Mp=0.254. Using the gain K from part (a), compute the parameter α of a lag compensator so that the steady-state error to a unit step reference input is  0.02. Determine τI such that the desired phase margin does not change too much. Does the choice of τI affect the steady-state error?   Do the work on paper showing all the steps (which you’ll submit later) but type below your K,  α  and τI

Choose the vector function below that represents the curve of intersection of the cylinder and the plane .

WARNING: The position function you were working with in the previous questions is changing! For the following 5 questions, let 

For the next five questions, let

Find the normal component of acceleration, , of the object whose position is given by . Enter the value of at , rounded to two decimal places.

What is the maximum height of the shot? Give your answer in feet and round to two decimal places.

If for all , then is orthogonal to for all .

If  for all , then is a constant.

If and are differentiable vector functions, then

How far down afield does the shot land? Give your answer in feet and round to two decimal places.