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    Coupled oscillators and normal modes question

    Homework Statement Two equal masses are held on a frictionless track by 3 equal springs, attached to two rigid posts. If either of the masses is clamped, the period (t=2pi/w) of one oscillation is three seconds. If both masses are free, what is the periods of oscillation of both normal...
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    Method of undetermined coefficients problem

    I have the problem "Find the particular solution of 4y''+4y'+y=3xex. What would be the assumed function y? Like would it be Ax ex?
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    Question about series and sequences

    The divergence test says that if the limit of a function is not 0, then it diverges. And the limit is 3/2, which is not 0, so it diverges..... right?
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    Question about series and sequences

    Homework Statement I have a function a_{n}=\frac{2+3n}{2n+1}, and I have to find out whether it converges or diverges. I did the ratio test lim_{n\rightarrow\infty}\left|\frac{a_{n+1}}{a_n}\right|. And according to the divergence test, it should diverge. Then it asks if the series...
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    Uncertain about volume of bounded region question

    I meant that the disks are stacked on top of eachother vertically.
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    Uncertain about volume of bounded region question

    Homework Statement The question states: Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. The lines are, y=lnX, y = 1, y = 2, and x = 0, rotated about the y-axis. I know how to integrate it, I just don't exactly know which...