A) \[\frac{\sqrt{3}}{2}\]
B) \[\frac{1}{\sqrt{2}}\]
C) \[\frac{3}{4}\]
D) \[\frac{1}{2}\]
Correct Answer: D
Solution :
Total energy \[{{E}_{T}}=\frac{1}{2}m{{\omega }^{2}}{{A}^{2}}\] \[{{E}_{k}}=\frac{1}{2}m{{\omega }^{2}}({{A}^{2}}-{{y}^{2}})\] \[=\frac{1}{2}m{{\omega }^{2}}\left( {{A}^{2}}-\frac{{{A}^{2}}}{2} \right)\,\,\,\,\left( \because \,\,y=\frac{A}{\sqrt{2}} \right)\] \[{{E}_{k}}=\frac{1}{2}\left( \frac{1}{2}m{{\omega }^{2}}{{A}^{2}} \right)=\frac{{{E}_{T}}}{2}\] So, \[\frac{{{E}_{k}}}{{{E}_{T}}}=\frac{1}{2}\]
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