A) \[y=\frac{a}{\sqrt{2}}\]
B) \[y=\frac{a}{2}\]
C) \[y=\frac{a}{\sqrt{3/2}}\]
D) \[y=a\]
Correct Answer: B
Solution :
Total energy, \[E=\frac{1}{2}m{{\omega }^{2}}{{a}^{2}};\] \[K.E.=\frac{3E}{4}=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}}).\] So, \[\frac{3}{4}=\frac{{{a}^{2}}-{{y}^{2}}}{{{a}^{2}}}\] or \[{{y}^{2}}=\frac{{{a}^{2}}}{4}\] or \[y=\frac{a}{2}\].
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