A) \[a\sqrt{2}\]
B) \[\frac{a}{2}\]
C) \[\frac{a\sqrt{2}}{3}\]
D) \[\frac{a}{\sqrt{2}}\]
Correct Answer: D
Solution :
When a body executes SHM it has both potential energy\[(U)\]and kinetic energy\[(K)\]given by \[U=\frac{1}{2}m{{\omega }^{2}}{{y}^{2}}\] where m is mass,\[\omega \]the angular speed and y the displacement. Also, \[K=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}})\] where a is amplitude. Given, \[K=U\] \[\therefore \] \[\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}})=\frac{1}{2}m{{\omega }^{2}}{{y}^{2}}\] \[\Rightarrow \] \[{{a}^{2}}=2{{y}^{2}}\] \[\Rightarrow \] \[y=\frac{a}{\sqrt{2}}\]
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