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Consider the following statements about a particle in simple harmonic motion: I. The acceleration of the particle is directly proportional to its displacement from the mean position and is directed towards the mean position. II. The velocity of the particle is maximum at the mean position. III. The total energy of the particle remains constant throughout the motion. IV. The period of SHM depends on the amplitude of o

Options

  1. AI, II, and III
  2. BII and III only
  3. CI, II, III, and IV
  4. DI and IV only

Correct answer

A. I, II, and III

Step-by-step solution

- Statement I: Correct - In SHM, acceleration is given by (a=- ^2 x ), where (x ) is the displacement and ( ) is the angular frequency. This shows that acceleration is directly proportional to displacement and is directed towards the mean position (negative sign). - Statement II: Correct - The velocity in SHM is maximum at the mean position because all the potential energy is converted into kinetic energy at this point. - Statement III: Correct - The total energy in SHM (sum of kinetic and potential energy) remains

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