Question

A particle starts simple harmonic motion from the mean position. Its amplitude is a and total energy E. At one instant its kinetic energy is $3E/4.$ Its displacement at that instant is

• A. $\mathbf{1/}\sqrt{\mathbf{2}}$
• B. $\mathbf{a/2}$
• C. $\frac{\mathbf{a}}{\sqrt{\mathbf{3/2}}}$
• D. $\mathbf{a/}\sqrt{\mathbf{3}}$

Answer 1

Answer: (B)

$\mathbf{a/2}$

Answer 2

$\frac{K}{E} = \frac{\frac{1}{2}m\omega^{2}(a^{2} - y^{2})}{\frac{1}{2}m\omega^{2}a^{2}} = \frac{a^{2} - y^{2}}{a^{2}} = 1 - \frac{y^{2}}{a^{2}}$

So, $\frac{\left( \frac{3E}{4} \right)}{E} = 1 - \frac{y^{2}}{a^{2}} \Rightarrow \frac{y^{2}}{a^{2}} = 1 - \frac{3}{4} = \frac{1}{4} \Rightarrow y = \frac{a}{2}$.