A particle simultaneously executes two mutually perpendicular SHMs of equal angular frequency: x = A cosωt and y = B cos(ωt+δ). Which statements are correct?
Select all that apply

Question

A particle simultaneously executes two mutually perpendicular SHMs of equal angular frequency: x = A cosωt and y = B cos(ωt+δ). Which statements are correct?

G1 Physics · Accepted Answer

For δ = 0, y/B = x/A, so the path is a straight line. For δ = π, y/B = −x/A, again a straight line. For δ = π/2, x/A = cosωt, y/B = −sinωt. Eliminating time gives x²/A²+y²/B² = 1, which is an ellipse. If A = B, the ellipse becomes a circle. Therefore all four statements are correct.