A particle is executing simple harmonic motion. Which one of the following statements about the acceleration of the oscillating particle is true ?
[amp_mcq option1=”It is always in the opposite direction to velocity” option2=”It is proportional to the frequency of oscillation” option3=”It is minimum when the speed is maximum” option4=”It decreases as the potential energy increases” correct=”option3″]
This question was previously asked in
UPSC NDA-2 – 2016
In simple harmonic motion, the acceleration of the oscillating particle is minimum when the speed is maximum.
Simple Harmonic Motion (SHM) is characterized by an acceleration that is directly proportional to the displacement from the equilibrium position and is always directed towards the equilibrium position (a = -ω²x, where x is displacement and ω is angular frequency). The equilibrium position is where the displacement x = 0. At this point, the restoring force and acceleration are zero, representing the minimum magnitude of acceleration. In SHM, the speed of the particle is maximum at the equilibrium position (x=0) and zero at the extreme positions (maximum |x|). Thus, acceleration (minimum at x=0) is minimum when speed (maximum at x=0) is maximum.