Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along X-axis 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 x-axis
D. a straight line inclined at `45^(@)` to the x-axis

Answer

A

Explanation

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