The displacement of a particle along the x-axis is x = a sin²(ωt). The motion of the particle corresponds to:
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The displacement of a particle along the x-axis is x = a sin²(ωt). The motion of the particle corresponds to:

G1 Physics · Accepted Answer

Step 1: Use sin²θ = [1 − cos(2θ)]/2 to obtain x = a/2 − (a/2)cos(2ωt). Step 2: The equilibrium position is x₀ = a/2; define displacement ξ = x − a/2. Step 3: Then ξ = −(a/2)cos(2ωt), which satisfies d²ξ/dt² = −4ω²ξ. Step 4: Thus the motion is SHM about x = a/2 with angular frequency 2ω and frequency f = ω/π. Step 5: The source book prints answer (C); that differs from the standard mathematical SHM definition. Final answer: (A) simple harmonic motion of frequency ω/π.