Can you please help me to understand the concept of frequency response analysis of control system?

Generally, in root locus analysis the open loop gain is varied from zero to infinity and then the path of roots is identified. From the root loci, the relative stability of the system is concluded. It means that as the open loop gain is varied, the roots of characteristic equation are changes. At a particular value of open loop gain the roots of characteristic equation may be on RHS. Then the system is said to be unstable.

Similarly, the frequency response of the system is obtained by varying the frequency of input signal ω. Hence, it can be separated into magnitude function and phase function. The magnitude and phase will be real functions of ω. As the frequency of input signal is varying, the amplitude and phase of response will be modified by amplitude and phase of transfer function respectively. It means that when a frequency of input signal is changed, the amplitude of response is changing based on amplitude of transfer function of the system.

Now my doubt is amplitude of response changing means what about the roots of transfer function. Is the roots of transfer function are changing as in case of root locus method or remains constant? If the roots are changing, then how to understand this concept?

Can anyone please help me to understand this concept?

Thank you.