Which of the following quantities remains constant for a particle executing simple harmonic motion?

Solution

1. In simple harmonic motion, the total mechanical energy $E$ is the sum of kinetic energy $K$ and potential energy $U$.
2. The kinetic energy is given by $K=\frac{1}{2}m{v}^2$ and the potential energy by $U=\frac{1}{2}k{x}^2$.
3. As the particle oscillates, energy is continuously exchanged between kinetic and potential forms, but the total sum $E=K+U$ remains constant.
4. Quantities such as velocity, acceleration, and restoring force depend on the position $x$ and change continuously throughout the motion.
5. Hence the answer is (C).