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  4. A body performs SHM along the straight line segment A B C D E with C as the mid point of segment A E(A and E are the extreme position for the SHM). Its kinetic energies at B and D are each one fourth of its maximum value. If length of segment A E is 2 R, then the distance between B and D is

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Q. A body performs SHM along the straight line segment $A B C D E$ with $C$ as the mid point of segment $A E(A$ and $E$ are the extreme position for the SHM). Its kinetic energies at $B$ and $D$ are each one fourth of its maximum value. If length of segment $A E$ is $2 R$, then the distance between $B$ and $D$ isPhysics Question Image

Oscillations

Solution:

When the particle crosses $D$, its speed is half the maximum speed.
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$\therefore V=\frac{v_{\max }}{R} \sqrt{R^{2}-x^{2}}$
or $\frac{v_{\max }}{2}=\frac{v_{\max }}{R} \sqrt{R^{2}-x^{2}}$ or $x=\frac{\sqrt{3}}{2} R$
Distance $B D=2 x=\sqrt{3} R$