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It is the full blown case where we consider every final possible force which can act on the system. The differential equation in this case,
Mu'' + γu' + ku = F( t)
The displacement function here will be
u(t) = uc(t) + UP(t)
Here the complementary solution will be the solution to the free, damped case and the exact solution will be found using undetermined coefficients or variation of parameter that ever is most convenient to utilize.
There are a couple of things to see now about this case. First, from our work back into the free, damped case we identify that the complementary solution will come to zero as t increases.
Due to this the complementary solution is often termed as the transient solution in this case. Also, due to this behavior the displacement will start to look more and more like the exact solution as t raises and so the particular solution is frequently termed as the steady state solution or forced response.
Estimation of difference among population proportions Assume the two proportions be described by P1 and P2, respectively,Then the difference absolute between the two proportion
5a^2b^2-5ab(6)
Measures of Dispersion - The measures of dispersion are extremely useful in statistical work since they indicate whether the rest of the data are scattered away from the mean
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