A body performs SHM along the segment A BC D E with C the midpoint of A E ( A , E are the extreme positions). Its kinetic energies at B and D are each one fourth of its maximum value. If A E = 2 R , t

Question

A body performs SHM along the segment A BC D E with C the midpoint of A E ( A , E are the extreme positions). Its kinetic energies at B and D are each one fourth of its maximum value. If A E = 2 R , the distance between B and D is:

TestHub · Accepted Answer

K E = 4 1 ​ K E ma x ​ gives 2 1 ​ k ( R 2 − x 2 ) = 4 1 ​ ⋅ 2 1 ​ k R 2 , so x = ± 2 3 ​ ​ R . B D = 3 ​ R .

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