Wave Mechanics Question 561
Question: A particle is executing simple harmonic motion with amplitude A. When the ratio of its kinetic energy to the potential energy is $ \frac{1}{4} $ , its displacement from its mean position is
Options:
A) $ \frac{2}{\sqrt{5}}A $
B) $ \frac{\sqrt{3}}{2}A $
C) $ \frac{3}{4}A $
D) $ \frac{1}{4}A $
Show Answer
Answer:
Correct Answer: A
Solution:
[a]
$ \
Therefore ,\frac{\frac{1}{2}m{{\omega }^{2}}(A^{2}-x^{2})}{\frac{1}{2}m{{\omega }^{2}}x^{2}}=\frac{1}{4}\Rightarrow \frac{A^{2}-x^{2}}{x^{2}}=\frac{1}{4} $
$ 4A^{2}-4x^{2}=x^{2}\Rightarrow x^{2}=\frac{4}{5}A^{2}\Rightarrow x=\frac{2}{\sqrt{5}}A. $
BETA
