SHMHard
Question
A particle moves in x-y plane according to rule x = a sin ωt and y = a cos ωt. The particle follows
Options
A.an elliptical path
B.a circular path
C.a parabolic path
D.a straight line path inclined equally to x and y axis
Solution
x = a sin ωt or 
= sin ωt
y = a cosωt or
= cos ωt
Squaring and adding, we get
(∵ cos2 ωt + sin2 ωt = 1)
or x2 + y2 = a2
this is the equation of a circle. Hence particle follows a circular path.
= sin ωty = a cosωt or
= cos ωt Squaring and adding, we get
(∵ cos2 ωt + sin2 ωt = 1) or x2 + y2 = a2
this is the equation of a circle. Hence particle follows a circular path.
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