A) \[\frac{1}{\sqrt{2}}\]
B) \[\frac{\sqrt{3}}{2}\]
C) \[\frac{1}{2}\]
D) \[\sqrt{2}\]
Correct Answer: A
Solution :
Given \[K.E.\,\,=\,\,P.E.\,\,\Rightarrow \,\,\frac{1}{2}\,m{{v}^{2}}\,\,=\,\,\frac{1}{2}\,k{{x}^{2}}\] \[\Rightarrow \,\,\frac{1}{2}\,m{{\omega }^{2}}({{a}^{2}}-{{x}^{2}})\,\,=\,\,\frac{1}{2}\,m{{\omega }^{2}}{{x}^{2}}\] \[\Rightarrow \,\,{{a}^{2}}-{{x}^{2}}={{x}^{2}}\Rightarrow {{x}^{2}}=\frac{{{a}^{2}}}{2}\,\,\Rightarrow \,\,\frac{x}{a}=\,\frac{1}{\sqrt{2}}\]
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