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