What do you mean?

If you have a transient system

[K]x(t) + [C]v(t) - [M]a(t) = F(t)

you can make a monochromatic expansion for a given frequency w

[K]x(w) + w[C]x(t) - w^2[M]x(t) = F(w).

So you solve for different frequencies w and with a convolution between the Fourier Transform of F(t) and the Transfer function you can have the solution in the time domain.

Regards,

Nicolás

Yeap that seems good approach. Here the entire problem is either in frequency domain or in time domain. And then the solution is sought for displacements

Consider that the solution for one such transient problem is already derived.

The displacements are found in transient domain. Now, if I need the displacement functions in the frequency domain, I would go for Fourier transformation of the displacements found in transient domain. This will provide the solution of that impulse force in frequency domain.

Am I right here!!!

Please do elaborate

Regards,

Hardik

Does anyone have bibliography of this subject?

Nicolás, your description is 99% agreeable, except I suggest an amendment to the second equation.

>> If you have a transient system

>> [K]x(t) + [C]v(t) - [M]a(t) = F(t)

>> you can make a monochromatic expansion for a given frequency w

>> [K]x(w) + w[C]x(t) - w^2[M]x(t) = F(w).

The monochromatic expansion to the time-domain system should be sought by Fourier transform of the entire left and right sides. If the system is linear (say if K C and M are constants, or perhaps they have Fourier transforms), then it will separate into single frequency components. Once this step is complete, all functions x(t) in the monochromatic equation should be in terms of their Fourier counterpart X(w), and no x(t) will remain.

Michael, you are right. My mistake, thanks!