# Effect of Damping on Steady State Vibration:Harmonic Excitation

1. Nov 26, 2006

### jrm2002

Considering the response of a single degree of freedom system to harmonic excitation with viscous damping , following conclusions can be drawn:

Now,

The response of a single degree of freedom system to harmonic excitation can be split into:

a) Steady Sate response (or vibration) which is a result of the applied force.
b)Transient vibration which is the the result of the free vibration and is dependent on the initial conditions.Right?

Now, the transient vibration decays with time as a consequence of damping.Right?

But, it is also observed that the amplitude of the steady state response incraeses with time.This can be mathematically be proved easily as a consequence of the solution of the differential equation.

My question is:

1)What is the physical reasoning for the amplitude of the steady state response increasing with time?

Besides,
It is also found that the amplitude of the steady stae response is more in systems without damping (a theoretical case though) and is less in systems with damping.Right?

My question is:

2)That means, damping palys a role in reducing the amplitude of both steady state response as well as transient response?But, the transient (free vibration) response eventually decays completely as a consequence of dapming.Right?
Can anyone throw some more light on this???