Particle X oscillates with the wave's period T, starting from its t=0 displacement.

Steps:

• Identify particle X's position and displacement from the t=0 snapshot graph.
• Recognize that in a transverse wave, each particle performs simple harmonic motion (SHM) with period T and amplitude equal to the wave's amplitude.
• Determine the phase: X's motion is sinusoidal, beginning at its initial displacement and velocity (zero if at crest/trough).
• Match the time graph to a sine/cosine wave with period T that aligns with X's starting point.

Why C is correct:

• Graph C depicts SHM with period T, starting from X's exact t=0 displacement, per the SHM equation y = A sin(2πt/T + φ), where φ matches the snapshot phase.

Why the others are wrong:

• A: Incorrect period, violates wave's T.
• B: Wrong initial displacement, doesn't match t=0 snapshot.
• D: Inverted phase or amplitude, contradicts transverse wave direction.

Final answer: C