The equation of the system is given as follows: 5yO) + 4y(t) =4F(t) dt (a) (i) Determine the sensitivity (dy/dt) and (ii) time constant (t) for the system (b) Formulate the general solution of the...

Extracted text: The equation of the system is given as follows: 5yO) + 4y(t) =4F(t) dt (a) (i) Determine the sensitivity (dy/dt) and (ii) time constant (t) for the system (b) Formulate the general solution of the differential equation if a 3U(t) step input is applied the system and IC Y(0)=0 Solution: The general equation for the first order system is given by dy(t) + aqy(t) = b,x(t) if dy(t) dt dt a1 dt dy(t) + a,y(t) = b,x(t) =5"YO + 4y(t) =4F(t) dt b, (a)(i): Static (steady state value) sensitivity of the system: k = (a)(ii) Hence Time Constant (in seconds) of the system: t: = 1.25 sec 4 The Equation can be written as 1.25 dye) + y(t) =F(t) dt (b) For Step Input 3 U(t)