Q.
The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of π results in the displacement of the particle along
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a
Straight line
b
Circle
c
Ellipse
d
Figure of eight
answer is A.
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Detailed Solution
Let us consider two simple harmonic motion y=bsinωt ……………………..(1)x=asinωt+ϕ ………………………(2)x=asinωtcosϕ+acosωtsinϕ From (1) yb=sinωt and 1−y2b2=cos ωt Substituting these is equation (2) we get xa=ybcosϕ+1−y2b2sinϕ Taking square on both sides we get xa−ybcosϕ2=1−y2b2sinϕ2Thus xa2+yb2cos2ϕ−2xyabcosϕ=1−y2b2sin2ϕ Simplifying this we getxa2+yb2−2xyabcosϕ=sin2ϕIn this case xa2+yb2+2xyabcosϕ=0 xa+yb2=0 Simplifying we get y=−xabMaking the equation a straight line
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