Question

A body executes simple harmonic motion with an amplitude $A$. At what displacement from the mean position is the potential energy of the body is one fourth of its total energy ?

• A. A / 4
• B. A/2
• C. 3A/4
• D. Some other fraction of A

Answer 1

Answer: (B)

$P.E =\frac{1}{2} M \omega^{2} x^{2}=\frac{1}{4} E=\frac{1}{4}\left(\frac{1}{2} M \omega^{2} A^{2}\right)$
where total energy $E =\frac{1}{2} M \omega^{2} A^{2}$
$ \therefore x=\frac{A}{2}$