i have attached two image, in first image there is no, omega term.. how in later steps the omega term came, please see attachments.
in equation 87, there is no omega term,
but later in equation 92 omega term came, how it is
Hey Naveen,
I think that's a typesetting error (which can happen in every good book).
When you assume the same harmonic time dependence for T as for u
(I am skipping the indices here):
dt2 T = - w2 T
and start from eq. (A-87) (independently of the actual form of u) you obtain the denominator of eq. (A-93).
T = -1/(p2-w2) F dt2u
IF the additional w2 in eq. (A-92) was correct, the denominator would be different. From the excerpt you attached, I therefore conclude this is extra term is an error overlooked in the editing process.
Hope that helps!
Regards.
thank you
dt2 T = - w2 T , can i know how this, i tried but dint get,
Dear Naveen,
eq. (A-93) is the mathematical solution to eq. (A-92) [without the error of an additional w2). You arrive at this solution by "guessing" that T has some amplitude and a harmonic time dependence:
T = T0 sin (wt)
then you insert this and arrive at eq. (A-93).
A physical system that is driven by an external source of a specific time dependence [here sin(wt), eq. (A-89)) typically takes on the same time dependence, hence, this was a good "guess", it gives a valid solution to eq. (A-92).
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