Question: A particle at position r(t) moves so that its acceleration at any time t is related to the position by r''(t) = -5r(t). Prove that

A particle at position r(t) moves so that its acceleration at any time t is related to the position by r''(t) = -5r(t). Prove that ||r'(t)|| + 5||r(t)||^2 is constant, independent of t using the identity w dot w = ||w||^2 and a product rule for derivatives.

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