The correct answer is: A. Root locus
Root locus is a graphical method in control theory that allows engineers to analyze the stability of a feedback system. It is a plot of the roots of the characteristic equation of the system as a function of a parameter, such as the gain of a controller. The root locus can be used to determine the stability of the system, as well as the range of values of the parameter for which the system is stable.
Bode plot is a graphical representation of the frequency response of a system. It is a plot of the magnitude and phase of the system’s transfer function as a function of frequency. The Bode plot can be used to determine the stability of the system, as well as the frequency response of the system.
Nyquist plot is a graphical representation of the frequency response of a system in polar coordinates. It is a plot of the magnitude and phase of the system’s transfer function as a function of frequency, with the magnitude on the radius and the phase on the angle. The Nyquist plot can be used to determine the stability of the system, as well as the frequency response of the system.
In conclusion, root locus is the best method for determining the stability and transient response of a system.