When a body is excited by an external force(forced Vibrations) there will be two components of the response of the body i.e Transient component and steady state component. this will be obvious when we look at the derivations of the equations of motion of the vibrating Structures.
The Presence of the Transient component owes to the inherent damping present in the body.After a certain period of time This transient response settles down and the response enters into a steady state.
harmonic analysis is used to study the steady state response of a structure while transient analysis is used to study the transient response of the structure.
The amplitude of the response of the structure at resonance i.e when the external frequency matches with one of the natural frequencies of the structure, often exceeds the static response by a factor which depends on the damping ratio.
The Finite One 