A particle is acted simultaneously by mutually perpendicular simple harmonic motions x = a cos ω t and y = a sin ω t . The trajectory of motion of the particle will be

Question

A particle is acted simultaneously by mutually perpendicular simple harmonic motions x = a cos ω t and y = a sin ω t . The trajectory of motion of the particle will be (A) an ellipse (B) a parabola (C) a circle (D) a straight line

Tardigrade Admin · Accepted Answer

Given x =a cos ω t ...(i) y=a sin ω t ...(ii) Squaring and adding (i) and (ii), we get x2 + y2 = a2cos2ω t + a2sin2ω t = a2 It is an equation of circle. Thus, trajectory of motion will be circle.

Q. A particle is acted simultaneously by mutually perpendicular simple harmonic motions $x = a cos ω t$ and $y = a s in ω t$ . The trajectory of motion of the particle will be

an ellipse

a parabola

a circle

a straight line

Given
$x = a cos ω t ... (i)$
$y = a s inω t ... (ii)$
Squaring and adding $(i)$ and $(ii)$ , we get
$x^{2} + y^{2} = a^{2} co s^{2} ω t + a^{2} s i n^{2} ω t = a^{2}$
It is an equation of circle. Thus, trajectory of motion will be circle.

Q. A particle is acted simultaneously by mutually perpendicular simple harmonic motions x=acosωt and y=asinωt . The trajectory of motion of the particle will be