To understand the displacement x0 where kinetic energy (KE) equals potential energy (PE) in simple harmonic motion (SHM), consider the following explanation: At the position x0, the kinetic energy is equal to the potential energy. Mathematically, this is represented by: ‌
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2
mω2(A2−x2)=‌
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mω2x2 Here, the left side of the equation represents the kinetic energy, and the right side represents the potential energy. Simplifying the equation: A2−x2=x2 Rearranging terms, we get: A2=2x2 Solving for x : ‌x2=‌