Which of the following graphs indicates the variation in kinetic energy of a particle executing simple harmonic motion?
Correct answer: B. Option B: A parabolic graph showing a squared relation.
- A. Option A: A sinusoidal graph showing periodic variation.
- B. Option B: A parabolic graph showing a squared relation.
- C. Option C: A linear graph showing a direct proportion.
- D. Option D: A constant graph showing no variation.
Explanation
The correct answer is Option B. In simple harmonic motion, the kinetic energy (KE) of a particle is given by the equation KE = (1/2)mv², where 'v' is the velocity of the particle. The velocity is maximum at the equilibrium position and zero at the maximum displacement positions, leading to a parabolic variation of kinetic energy with respect to displacement, which is depicted by a squared relation. Option A is incorrect because a sinusoidal graph represents functions like displacement or velocity over time, not kinetic energy. Option C is incorrect because kinetic energy does not vary linearly; it depends on the square of the velocity. Option D is incorrect because the kinetic energy is not constant; it varies periodically.
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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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