Motion of a particle in x-y plane is described by a set of following equations x=4sin⁡π2−ωtm and y=4sin⁡(ωt)m. The path of the particle will be :

x=4sin⁡π2−ωt=4cos⁡(ωt)x=4cos⁡(ωt) y=4sin⁡(ωt)Eliminate ‘t’ to find relation between x and y x2+y2=42cos2⁡ωt+42sin2⁡ωt=42x2+y2=42

Motion of a particle in x-y plane is described by a set of following equations x=4sin⁡π2−ωtm and y=4sin⁡(ωt)m. The path of the particle will be :

x=4sin⁡π2−ωt=4cos⁡(ωt)x=4cos⁡(ωt) y=4sin⁡(ωt)Eliminate ‘t’ to find relation between x and y x2+y2=42cos2⁡ωt+42sin2⁡ωt=42x2+y2=42

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Motion of a particle in x-y plane is described by a set of following equations $x = 4 \sin (\frac{π}{2} - ω t) m$ and $y = 4 \sin (ω t) m$ . The path of the particle will be :

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circular

helical

parabolic

elliptical

answer is A.

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Detailed Solution

$\begin{array}{l} x = 4 \sin (\frac{π}{2} - ωt) = 4 \cos (ωt) \\ x = 4 \cos (ωt) y = 4 \sin (ωt) \end{array}$
Eliminate ‘t’ to find relation between x and y
$\begin{array}{l} x^{2} + y^{2} = 4^{2} \cos^{2} ωt + 4^{2} \sin^{2} ωt = 4^{2} \\ x^{2} + y^{2} = 4^{2} \end{array}$