Which one of the following four particles, whose displacement x and acceleration a, are related as follows, is executing simple harmonic motion?
a = +3x
a = +3x²
a = -3
a = -3x
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-2 – 2016
Simple Harmonic Motion (SHM) is defined by a linear restoring force proportional to the displacement from the equilibrium position and directed towards it. According to Newton’s second law (F = ma), this implies that the acceleration is also proportional to the displacement and directed towards the equilibrium position. The general form of the acceleration-displacement relationship for SHM is a = -ω²x, where ω² is a positive constant (related to the system’s properties like mass and stiffness). Option D, a = -3x, fits this form with ω² = 3 (or ω = √3).