A) 33
B) 87
C) 67
D) 50
Correct Answer: B
Solution :
Kinetic energy\[=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}})\] Potential energy\[=\frac{1}{2}m{{\omega }^{2}}y\] \[=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}})\] \[=\frac{1}{3}\times \frac{1}{2}m{{\omega }^{2}}{{y}^{2}}\] \[\frac{4}{6}m{{\omega }^{2}}{{y}^{2}}=\frac{1}{2}m{{\omega }^{2}}{{a}^{2}}\] \[{{y}^{2}}=\frac{3}{4}{{a}^{2}}\] \[y=\frac{\sqrt{3}\,a}{2}-0.866\,a\] \[=\] 87% of amplitude
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