A) \[\frac{2}{\sqrt{5}}A\]
B) \[\frac{\sqrt{3}}{2}A\]
C) \[\frac{3}{4}A\]
D) \[\frac{1}{4}A\]
Correct Answer: A
Solution :
[a] \[\therefore \,\,\,\frac{\frac{1}{2}m{{\omega }^{2}}({{A}^{2}}-{{x}^{2}})}{\frac{1}{2}m{{\omega }^{2}}{{x}^{2}}}=\frac{1}{4}\Rightarrow \frac{{{A}^{2}}-{{x}^{2}}}{{{x}^{2}}}=\frac{1}{4}\] \[4{{A}^{2}}-4{{x}^{2}}={{x}^{2}}\Rightarrow {{x}^{2}}=\frac{4}{5}{{A}^{2}}\Rightarrow x=\frac{2}{\sqrt{5}}A.\]
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