Physics · Simple harmonic motion (S.H.M.) and its equation, phase
A particle is acted simultaneously by mutually perpendicular simple harmonic mot
A particle is acted simultaneously by mutually perpendicular simple harmonic motions \( x=a c o s \omega t \) and \( y= \) asinwt. The trajectory of motion of the particle will be
- A. an ellipse
- B. a parabola
- C. a circle
- D. a straight line
Step-by-step solution
The parametric equations x = a cos ωt and y = a sin ωt satisfy x^2 + y^2 = a^2 (since cos^2 ωt + sin^2 ωt = 1). This is the equation of a circle with radius a centered at the origin. Therefore, the trajectory is a circle.
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