A particle is subjected to two simple harmonic motions along x and y directions according to `x=3sin100pit`, `y=4sin100pit`.

Options

A. Motion of particle will be on ellipse travelling in clockwise direction.
B. Motion of particle will be on a straight line with slope `(4)/(3)`
C. Motion will be simple harmonic motion with amplitude 5.
D. Phase difference between two motions is `(pi)/(2)`

Answer

B, C

Explanation

`x=3sin100pit`
`y=4sin100pit`
Equation of path is `(y)/(x)=(4)/(3)`
i.e., `t=(4)/(3)x`
which is equation of a straight line having slope `(4)/(3)`. Equation of resulting motion is
`vecr=xhati+yhatj=(3hati+4hatj)sin100pit`
Amplitude`=sqrt(3^2+4^2)=5`