Q.

A body performs SHM along the straight line segment ABCDE with c as the mid point of segment AE (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. The length of segment AE is 2R, if the distance between B and, D is found to be xR . The value of x is __________.

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answer is 3.

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Detailed Solution

When the particle crosses point D, its speed is half of the maximum speed. Given that amplitude is 2R⇒ v=vmaxRR2−x2 or  vmax2=vmaxRR2−x2 or  x=32R⇒ Distance BD=2x=3R Hence x=3
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A body performs SHM along the straight line segment ABCDE with c as the mid point of segment AE (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. The length of segment AE is 2R, if the distance between B and, D is found to be xR . The value of x is __________.