Kinetic energy proportional to squared velocity in oscillatory motion

Steps:

• Displacement-time graph is sinusoidal, representing simple harmonic motion of the air particle.
• Velocity is the derivative of displacement, yielding a cosine wave (positive and negative).
• Kinetic energy KE = ½ m v², so KE varies as the square of velocity, always non-negative.
• Squaring the velocity produces a waveform oscillating at twice the frequency of displacement, between zero and maximum.

Why D is correct:

• D depicts the squared cosine variation, directly following KE ∝ v² from Newton's laws of motion.

Why the others are wrong:

• A: Mirrors displacement, which includes negative values unlike energy.
• B: Resembles velocity, which oscillates through zero but goes negative.
• C: Shows constant or linear trend, ignoring oscillatory nature of v².

Final answer: D