NEET
- Exam
- NEET
- Subject
- Physics
- Chapter
- Oscillations
NEET · Physics · Oscillations
Consider the following statements about a particle in simple...
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 oscillation.
Which of the above statements are correct?
Options
- AI, II, and III
- BII and III only
- CI, II, III, and IV
- 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=-\omega^2 x), where is the displacement and (\omega) 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 constant as it is conserved, assuming no friction or resistance.
- Statement IV: Incorrect
- The time period of SHM is independent of amplitude. It only depends on the mass and spring constant (in spring systems) or the length and gravity (in pendulum systems).
Thus, the correct combination of statements is I, II, and III.