Final answer:
The time taken by a particle in simple harmonic motion to move from an extreme position to halfway towards its equilibrium position is a quarter of the period, which is T/4. Option B is correct.
Step-by-step explanation:
The question involves finding the time taken by a particle executing simple harmonic motion (SHM) to move from an extreme position to halfway towards its equilibrium position.
The formula to find the period (T) of a simple harmonic oscillator is given by T = 2π√(m/k), where m is the mass of the oscillator and k is the spring constant. However, the question specifically pertains to the time it takes to cover a certain portion of that period.
In SHM, the motion of a particle is equivalent to the projection of uniform circular motion onto a diameter. Since the particle starts at the extreme position, it starts at the top of the circular path in this analogy. Moving halfway to the equilibrium position corresponds to moving a quarter of the way around the circular path, which is a quarter of the period. Therefore, the correct answer is T/4.
The time taken by a particle executing simple harmonic motion to reach from the extreme position to halfway between the extreme positions is T/4. In simple harmonic motion, the particle oscillates back and forth symmetrically about the equilibrium position. The time period T represents the time taken for one complete oscillation. So, the time taken to reach halfway between the extreme positions is one-fourth of the time period, which is T/4.