A) \[\frac{1}{2}\]
B) \[\frac{1}{4}\]
C) \[\frac{1}{\sqrt{2}}\]
D) \[\frac{3}{4}\]
Correct Answer: D
Solution :
In SHM, kinetic energy \[K=\frac{1}{2}m{{\omega }^{2}}({{A}^{2}}-{{x}^{2}})\] where, A is the amplitude of the condition At \[x=\frac{1}{2}A\] \[K=\frac{1}{2}m{{\omega }^{2}}\left[ {{A}^{2}}-{{\left( \frac{A}{2} \right)}^{2}} \right]\] \[=\frac{3}{4}\times \frac{1}{2}m{{\omega }^{2}}{{A}^{2}}\] Total energy, \[E=\frac{1}{2}m{{\omega }^{2}}{{A}^{2}}\] \[\therefore \] \[\frac{K}{E}=\frac{3}{7}\]
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