If x is the displacement of a bob of a simple pendulum from the mean position, then kx2/2 will be equal to itsI. total energyII.kinetic energyIII. potential energy
Correct answer: D. II and III.
- A. I only.
- B. III only.
- C. I and II.
- D. II and III.
Explanation
The expression kx²/2 is a form of energy that can be interpreted in the context of a simple pendulum's motion. In classical mechanics, this expression typically represents the potential energy in a system where k is a constant and x is the displacement. However, for a simple pendulum, as it swings, the displacement x from the mean position can contribute to both kinetic and potential energy depending on the phase of the pendulum's motion. Therefore, option D, 'II and III,' is correct. The potential energy is maximal at the maximum displacement, while kinetic energy is maximal at the mean position. Options A, B, and C are incorrect as they do not fully capture the dual role of displacement in contributing to both forms of energy in this context.
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About Simple Harmonic Motion
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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