Simple harmonic motion – travel from one extremity to the other corresponds to what fraction of an oscillation? For a body in SHM, the motion from one extreme position through the mean to the opposite extreme constitutes what portion of a complete oscillation?

Introduction / Context:
Understanding the timing of simple harmonic motion (SHM) is crucial in vibration analysis and timing devices. The phase relationships between extreme and mean positions define how long each segment of motion takes relative to the period.

Given Data / Assumptions:

• Small-amplitude SHM obeying x = A cos(ωt + φ).
• Period T = 2π/ω; extremes occur at x = ±A.
• Motion is continuous and undamped.

Concept / Approach:

One full oscillation is the motion returning to the same position with the same direction of velocity after time T. The time from one extreme to the opposite extreme is the time taken to traverse half a cycle in phase.

Step-by-Step Solution:

Verification / Alternative check:

Plotting x versus t for SHM shows symmetries every T/2 between opposite extremes and every T between identical states (same position and direction).

Why Other Options Are Wrong:

(b) One full oscillation requires returning to the starting extreme with the same velocity direction, which takes T, not T/2. (c) Two oscillations correspond to 2T. (e) One quarter T only gets from an extreme to the mean.

Common Pitfalls:

Confusing “passing the mean” with completing a full cycle; forgetting the symmetry of cosine/sine over π radians for half a period.

Final Answer:

half an oscillation