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Question

A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by x=2sinωt ; y=2sin(ωt+π4). The path of the particle will be:

A
an ellipse
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B
a straight line
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C
a parabola
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D
a circle
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Solution

The correct option is A an ellipse
x=2sinωt;y=2sin(ωt+π4)
sinωt=x2 .....(I)
cosωt=1sin2ωt=1(x2)2=1x24 .....(II)
y=2sin(ωt+π4)y=2(sinωt+cosωt)2=2(sinωt+cosωt)
using the values of from (I) and (II), we have
y=2(x2+1x24)y2x2=1x24y22+x24xy2=1x24x22+y22xy21=0x2+y22xy2=0
which is an equation of an oblique ellipse.
164106_119436_ans.JPG

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