Asked in MDCAT Test Series 5 — Waves and Thermodynamics (7 March 2025) 2025Moderate

The restoring force of SHM is maximum when particle:

Correct answer: A. Displacement is maximum

  • A. Displacement is maximum
  • B. Half way between them
  • C. Crossing mean position
  • D. At rest

Explanation

The restoring force of Simple Harmonic Motion (SHM) is maximum when the displacement of the particle is maximum. In SHM, the restoring force is given by Hooke's Law: F = -kx Where: F is the restoring force, k is the spring constant, and x is the displacement of the particle from its equilibrium position. The negative sign indicates that the restoring force acts in the opposite direction to the displacement. Now, let's consider the particle's displacement at different points in its motion. When the particle is at the maximum displacement (either positive or negative), the value of x is at its maximum. If we substitute the maximum displacement value into the equation, we get: F = -k * xmax Since the displacement is at its maximum, the magnitude of the restoring force is also at its maximum.

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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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