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Q.

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

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a

motion of particle will be on ellipse travelling in clock wise direction 

b

motion of particle will be on straight line with slope  43

c

motion will be simple harmonic motion with amplitude 5

d

phase difference between two motions is  π2

answer is C, B.

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Detailed Solution

detailed_solution_thumbnail

 x=3som100πt
y=4sin100πt 
Equation of path is yx=43  i.e.,  y=43x
Which is equation of straight line having slope 43 
  equation of resulting motion is r¯=xi¯+yj¯=(3i¯+4j¯)sin100πt 
  amplitude = 32+42 =5

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