I would very much appreciate if anyone can help me with this problem; I have approached it from many different angles to no avail.(adsbygoogle = window.adsbygoogle || []).push({});

The position x(t) of a particle moving along the x-axis is governed by the differential

equation:

[tex]x'' + kx' + (n^2)x = 0[/tex] , and initially [tex]x(0) = a[/tex], [tex]x'(0) = u[/tex].

Show that:

[tex]

\int_{0}^{Infinity} x^{2}dt = \frac{1}{2kn^2}((u + ka)^2 + n^2a^2)

[/tex]

Show that, as a function of k, this is a minimum when:

[tex]k^2 = n^2 + \frac{u^2}{a^2}[/tex]

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# Homework Help: Second Order Homogeneous Differential Equation.

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