The potential energy of a simple harmonic oscillator when the particle is half way to its end point is (where $E$ is the total energy)
AIPMT 2003, Medium
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(b) $\frac{U}{E} = \frac{{\frac{1}{2}m{\omega ^2}{y^2}}}{{\frac{1}{2}m{\omega ^2}{a^2}}} = \frac{{{y^2}}}{{{a^2}}} = \frac{{{{\left( {\frac{a}{2}} \right)}^2}}}{{{a^2}}} = \frac{1}{4}$
==> $U = \frac{E}{4}$
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