A particle simultaneously executes two mutually perpendicular oscillations given by x = A cosωt and y = B cos2ωt. Which equation represents the trajectory after eliminating time?
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Question

A particle simultaneously executes two mutually perpendicular oscillations given by x = A cosωt and y = B cos2ωt. Which equation represents the trajectory after eliminating time?

G1 Physics · Accepted Answer

From x = A cosωt, we get cosωt = x/A. Also, y = B cos2ωt. Using the identity cos2φ = 2cos²φ−1, we obtain y = B[2cos²ωt−1]. Substitute cosωt = x/A: y = B[2x²/A²−1]. Thus the trajectory is a parabolic segment. Correct option: B.