When the displacement is half the amplitude, the ratio of potential energy to the total energy is
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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} $
$= \frac{1}{4}$
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