The position vector of a particle moving in space is r⃗ = [1 + 2 cos(2ωt)]î + [3 sin²(ωt)]ĵ + 3k̂ in the ground frame. Choose the correct statement(s).
Select all that apply

Question

The position vector of a particle moving in space is r⃗ = [1 + 2 cos(2ωt)]î + [3 sin²(ωt)]ĵ + 3k̂ in the ground frame. Choose the correct statement(s).

G1 Physics · Accepted Answer

Use sin²ωt=(1−cos2ωt)/2. Then r⃗=(1,3/2,3)+[2î−(3/2)ĵ]cos(2ωt). Therefore the particle executes SHM in the ground frame about mean position (1,3/2,3). The amplitude is √[2²+(3/2)²]=5/2 m, and the direction unit vector is (4/5)î−(3/5)ĵ. Thus A, C and D are correct; B is false.