A) zero
B) \[\frac{1}{2}\]
C) \[\frac{1}{4}\]
D) \[\frac{3}{4}\]
Correct Answer: C
Solution :
Total energy \[E=\frac{1}{2}m\,\,{{\omega }^{2}}\,{{a}^{2}}\] \[K.E.=\frac{1}{2}m\,{{\omega }^{2}}\,{{y}^{2}}\] According to question \[y=\frac{a}{2}\] \[=\frac{1}{2}m\,\,{{\omega }^{2}}{{a}^{2}}{{\left( \frac{y}{2} \right)}^{2}}\] \[=\frac{1}{2}m\,\,{{\omega }^{2}}\frac{{{a}^{2}}}{4}\] \[=\frac{1}{4}\left( \frac{1}{2}m\,{{\omega }^{2}}\,{{a}^{2}} \right)=\frac{1}{4}E\] Therefore, K.E, is \[\frac{1}{4}\] .times of total energy.
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