For each of the transfer functions below, plot the poles and zeros on a s-plane. find the damping ratio and state the nature of the response (overdamped, underdamped, finally, calculate the response of each system to a unit step input using inverse laplace transforms. state the nature of each response (overdamped, underdamped, and so on). then calculate the exact response of each system using laplace transform. then find the damping ratio and natural frequency for each second-order system and show that the value of the damping ratio conforms to the type of response (underdamped, overdamped, and so on).
(a) t(s)= {s}/{s+2}
(b) t(s)= {20}/{s^{2}+6s+144}
(c) t(s)= {(s+5)}/{(s+10)^{2}}

step-by-step explanation:

ddd

rotation point l

step-by-step explanation:

hard

step-by-step explanation:

one way is to plot 2 points and connect them which is what the answer choices seem to be doing

it seems to be using the y intercept and the slope

y=mx+b, m=slope, b=y-intercept (where the line hits the y axis)

slope=rise/run

y-intercept is where the line croses the y axis which is the y value where x=0

you seem to have given the wrong slope (you didn't put a number in front of te x, it should be 2/3 or 3/2 looking at the answer options)

y=? x-1

m=? because of your fault

b=-1

so it has a slope of ? and y intercept of -1, meaning it pases through (0,-1)

so draw point (0,-1) (so answer is one of the first 2 option)

if slope is 2/3, then go up 2 and right 3 then draw line through those 2 points

if slope is 3/2, then go up 3 and right 2 then draw line through those 2 points