Solution:
$P.E. = \frac{1}{4} E \Rightarrow \frac{1}{2} k x^2 = \frac{1}{4} (\frac{1}{2} k A^2) \Rightarrow x^2 = \frac{A^2}{4} \Rightarrow x = \frac{A}{2}$.
A body executes simple harmonic motion with an amplitude $A$. At what displacement from the mean position is the potential energy of the body is one fourth of its total energy? (1992)
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