Discussion
A particle executes linear simple harmonic motion and its potential energy (P.E), kinetic energy (K.E) and total energy (T.E) are measured as functions of displacement x from the mean position at the origin. Then
Answer: E
The correct statement is that P.E. is maximum when x is maximum.
In linear SHM, \(PE = \frac{1}{2}kx^{2}\) and \(KE = \frac{1}{2}k(A^{2} - x^{2})\), with total energy \(\frac{1}{2}kA^{2}\) constant. The potential energy is greatest at the extreme positions \(x = \pm A\), where the particle momentarily stops.
At \(x = 0\) the kinetic energy is maximum, not minimum, and the potential energy is zero, not maximum. The total energy is the same everywhere and never zero for an oscillating particle, and the kinetic energy is zero, not maximum, at maximum displacement.
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