Question

A particle starts SHM from the mean position. Its amplitude is a and total energy $ E $ . At one instant its kinetic energy is $ 3\frac{E}{4} $ . Its displacement at that instant is:

• A. $ \frac{a}{\sqrt{2}} $
• B. $ \frac{a}{2} $
• C. $ \frac{a}{\sqrt{\left( \frac{3}{2} \right)}} $
• D. $ \frac{a}{\sqrt{3}} $
• E. $ a $

Answer 1

Answer: (B)

$ k=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}}) $
$ \frac{3}{4}E=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}}) $
$ \frac{3}{4}\left( \frac{1}{2}m{{\omega }^{2}}{{a}^{2}} \right)=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}}) $
$ {{y}^{2}}={{a}^{2}}-\frac{3}{4}{{a}^{2}} $
$ =\frac{{{a}^{2}}}{4} $
$ \Rightarrow $ $ y=\frac{a}{2} $