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Question

A particle is subjected to two simple harmonic motion along x and y directions, according to equation x=3sin100πt;y=4sin100πt. Then,

A
motion of particle will be on ellipse travelling in clockwise direction.
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B
Motion of particle will be on a straight line with slope 43
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C
Motion will be a simple harmonic motion with amplitude 5.
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D
Phase difference between two motions is π2.
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Solution

The correct options are
B Motion of particle will be on a straight line with slope 43
C Motion will be a simple harmonic motion with amplitude 5.
Given
x=3sin100πt
y=4sin100πt
Equation of path is
yx=43
i.e. y=43x
which is equation of a straight line having slope 43
Equation of resulting motion is r=x^i+y^j
r=(3^i+4^j)sin100πt
Amplitude is 32+42=5
Why this question?

When particle undergoes multiple non collinear SHMs, a convinient way is to use vector analysis.

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