Simple harmonic motion (SHM) — definition of period: In engineering dynamics, the periodic time (time period) of a particle executing simple harmonic motion is defined as the time taken by the particle to complete which part of its oscillatory cycle?

Introduction / Context:
The term “period” (or periodic time) is fundamental in vibration analysis, machine dynamics, and structural engineering. For simple harmonic motion (SHM), such as a mass–spring or small-angle pendulum, correctly identifying what one period represents is essential for timing, resonance, and frequency calculations.

Given Data / Assumptions:

• The motion is ideal SHM with no damping.
• The particle oscillates symmetrically about an equilibrium (mean) position.
• Terminology: cycle, oscillation, amplitude, frequency, and period are used in their standard engineering sense.

Concept / Approach:

One period T is the time for the motion to repeat itself. For SHM this means the particle returns to the same displacement, velocity, and acceleration states. Frequency f is the number of complete oscillations per second, and T = 1 / f. Hence, a “complete oscillation” is the precise descriptor of one period.

Step-by-Step Solution:

Verification / Alternative check:

Using sinusoidal representation x(t) = A cos(ωt + φ), period T = 2π/ω is the smallest positive time for which x(t + T) = x(t), v(t + T) = v(t), and a(t + T) = a(t).

Why Other Options Are Wrong:

Half or quarter oscillation (a, b) do not return the system to the same complete state; “none of these” (d) and “one and a half oscillations” (e) are definitional mismatches.

Common Pitfalls:

Confusing “time from one extreme to the other” (T/2) with the full period; mixing up angular frequency ω and cyclic frequency f.

Final Answer:

complete oscillation