Question
Abody performs simple harmonic oscillations along the straight line $ABCDE$ with $C$ as the midpoint of $AE.$ Its kinetic energies at $B$ and $D$ are each one fourth of its maximum value. If $AE = 2R,$ the distance between $B$ and $D$ is
✓
Answer
$\frac{1}{2} k\left(A^{2}-x^{2}\right)=\frac{1}{4}\left(\frac{1}{2} k A^{2}\right)$
$\therefore x=\frac{\sqrt{3}}{2} A$
$\therefore C D=C B=\frac{\sqrt{3}}{2} R$
or $B D=2(C D)$
or $2(C B)=\sqrt{3} R$
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