Two simple harmonic motions with the same frequency act on a particle at right angles i.e, along x and y axis. If the two amplitudes are equal and the phase difference is `(pi)/(2)` the resultant motion will be :

Options

A. a circle
B. an ellipse with the major axis along y-axis
C. an ellipse with the major axis along y-axis
D. an straight line inclined at `45^(@)` to the x-axis

Answer

A

Explanation

Equation of two simple harmonic motion
`Y=A sin (omegat+ phi) " "....(1)`
`x= A sin (omega+phi+(pi)/(2))`
`x=A cos (omegat+phi) " "....(2)`
On squaring and adding equations (1) & (2)
. `x^(2)+y^(2)=A^(2)`
This is an equation of a circle. Hence, resulting motion will be a circle motion.