A system described by the transfer functionis stable.  The constraints on 𝛼 and k are,Select one:a. 𝛼 < 0, 𝛼𝐾 > 3b. 𝛼 > 0, 𝛼𝐾 < 3c. 𝛼 < 0, 𝛼𝐾 < 3d. 𝛼 > 0, 𝛼𝐾 > 3

the feedback system with the characteristic equation 2s4 + 20ks3 + 3s2 + 5s + 7 = 0(a)stable for all value of k(b)stable fo rpositive value of k(c)stable for infinity>k>7.0(d)unstable for all values of k

Parameters of the following transfer function are given as: k=3.1, a=9.8, and b=4.2, calculate the gain constant K of the control system. (please keep four digits after decimal point)𝑇𝐹=𝑘𝑎𝑠+𝑏

What are the general criteria for achieving unconditional stability?a.K>1 and |Δ||Δ|<1b.K<1 and |Δ||Δ|<1c.K>1 and |Δ||Δ|>1d.K<1 and |Δ||Δ|>1

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)

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 − 2𝑒 −2𝑡 ) 𝑢(𝑡)b. (0.5 + 2𝑒 −𝑡 + 2𝑒 −2𝑡 ) 𝑢(𝑡)c. (0.5 + 𝑒 −𝑡 + 1.5𝑒 −2 ) 𝑢(𝑡)d. (1 − 2𝑒 −𝑡 + 𝑒 −2 ) 𝑢(𝑡)