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Question

A particle is subjected to two simple harmonic motions along x and y directions according to x=3 sin100πt andy=4 sin100πt. Choose the correct statement(s).

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 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 simple harmonic motion with amplitude 5.
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=(3^i+4^j)sin100πt
Amplitude=32+42=5

Phase difference between x and y motions is clearly zero.

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