A particle executing simple harmonic motion with amplitude a has the same potential and kinetic energies at the displacement:
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A particle executing simple harmonic motion with amplitude a has the same potential and kinetic energies at the displacement:

G1 Physics · Accepted Answer

Step 1: Total energy in SHM is E = ½ka². Step 2: Potential energy at displacement x is U = ½kx² and kinetic energy K = ½k(a² − x²). Step 3: For U = K, we have x² = a² − x², hence 2x² = a². Step 4: Therefore the magnitude of displacement is |x| = a/√2. Final answer: (C) a/√2.