Question

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Answer 1

if a body executes S.H.M. with an amplitude xo its energy is half kinetic and half potential when displacement is .
If the total energy is half Kinetic and half potential, it is true only if K=U
from the original condition, K=UK=U

Or,

12k(A2−x2)=12kx212k(A2−x2)=12kx2

⟹A2−x2=x2⟹A2−x2=x2

⟹2x2=A2⟹2x2=A2

⟹x2=A22⟹x2=A22

⟹x=±A2–√⟹x=±A2

At displacements ±A2–√±A2, the kinetic energy is equal to the potential energy.