A) \[\frac{1}{2}\]
B) \[\frac{3}{4}\]
C) \[\frac{1}{4}\]
D) \[\frac{1}{8}\]
E) \[\frac{1}{6}\]
Correct Answer: C
Solution :
\[E=\frac{1}{2}m{{\omega }^{2}}{{a}^{2}}\] \[U=\frac{1}{2}m{{\omega }^{2}}{{y}^{2}}\] \[\Rightarrow \] \[U=\frac{1}{2}m{{\omega }^{2}}\times {{\left( \frac{1}{2}a \right)}^{2}}\] \[\therefore \] \[U=\frac{1}{4}\times \frac{1}{2}m{{\omega }^{2}}{{a}^{2}}=\frac{1}{4}E\]
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