A) \[\propto x\]
B) \[\propto \,{{x}^{2}}\]
C) Independent of\[x.\]
D) \[\propto {{x}^{1/2}}\] where,\[x\]is the displacement from the mean position.
Correct Answer: C
Solution :
In simple harmonic motion when a particle is displaced to a position from its mean position, then its kinetic energy gets converted into potential energy. Hence, total energy of a particle remains constant or the total energy in simple harmonic motion does not depend on displacement\[x\]. It fact it depends on the amplitude. \[\because \]Total energy in\[SHM=\frac{1}{2}m{{\omega }^{2}}{{A}^{2}}=2{{\pi }^{2}}m{{A}^{2}}\].
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