Solution:
$K.E. = \frac{1}{2} k (a^2 - x^2)$. At $x = a/2$, $K.E. = \frac{1}{2} k (a^2 - a^2/4) = \frac{3}{4} (\frac{1}{2} k a^2) = \frac{3}{4} E$.
In a simple harmonic motion, when the displacement is one-half of the amplitude, what fraction of the total energy is kinetic? (1995)
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