A second order system is governed by y¨(t)+2y˙(t)=u(t)𝑦¨(𝑡)+2𝑦˙(𝑡)=𝑢(𝑡). Its transfer function is1s2+21𝑠2+21s2−21𝑠2−21s2+2s1𝑠2+2𝑠1s2−2s

The solution to the ordinary differential equation y˙(t)=−2y(t),y(0)=1,𝑦˙(𝑡)=−2𝑦(𝑡),𝑦(0)=1, isy(t)=−2e−2t𝑦(𝑡)=−2𝑒−2𝑡y(t)=2e−2t𝑦(𝑡)=2𝑒−2𝑡y(t)=e−2t𝑦(𝑡)=𝑒−2𝑡y(t)=−e−2t

A system described by the following differential equation   + 3  +2𝑦 = x(𝑡) is initially at rest. For input x(𝑡) = 2𝑢(𝑡), the output y(t) isSelect one:a. (1 − 2𝑒 −𝑡 + 𝑒 −2 ) 𝑢(𝑡)  b. (0.5 + 𝑒 −𝑡 + 1.5𝑒 −2 ) 𝑢(𝑡)c. (0.5 + 2𝑒 −𝑡 + 2𝑒 −2𝑡 ) 𝑢(𝑡)d. (1 + 2𝑒 −𝑡 − 2𝑒 −2𝑡 ) 𝑢(𝑡)

Which of the following choices is not a system equation of the following suspension system? Assume u is the displacement input, y is the displacement output; y>x>u; 𝑥′,𝑥″are the 1st order and 2nd order derivative of x, respectively.Group of answer choices𝐹𝑘1=𝑘1(𝑥−𝑢)All of the rest choices are correct system equations for the system𝐹𝑏=𝑏(𝑦′−𝑥′)𝐹𝑘2=𝑘2(𝑦−𝑥)𝐹𝑛𝑒𝑡1=𝑚1𝑥″

a linear second order single input continuous time system is described by following set of differential equation:x1(t) = -2x1(t) + 4x2 (t)x2(t) = 2x1(t) - x2 (t) + u(t)where x1(t) and x2(t) are state variable and u(t) is the control variable..................the system is:(a)controllable and stable(b)controllable but unstable(c)uncontrollable and unstable(d)uncontrollable but stable

For a second-order system with the closed-loop transfer function (𝑠) =               the settling time for 2-percernt band, in seconds, isSelect one:a. 1.5b. 4c. 2d. 3