Statement 1: Position–time equation of a particle moving along x-axis is x = 4 + 6 sin(ωt). Under this situation, motion of the particle is not simple harmonic. Statement 2: d²x/dt² for the given equation is not proportional to -x.
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Question

Statement 1: Position–time equation of a particle moving along x-axis is x = 4 + 6 sin(ωt). Under this situation, motion of the particle is not simple harmonic. Statement 2: d²x/dt² for the given equation is not proportional to -x.

Options

G1 Physics · Accepted Answer

Put X=x−4. Then X=6 sin(ωt), so Ẍ=−ω²X and the motion is SHM about x=4. But ẍ=−ω²(x−4), which is not proportional to −x measured from the original origin. Hence Statement 1 is false and Statement 2 is true. Correct answer: D.

Statement 1: Position–time equation of a particle moving along x-axis is x = 4 + 6 sin(ωt). Under this situation, motion of the particle is not simple harmonic. Statement 2: d²x/dt² for the given equation is not proportional to −x.