The resultant of two rectangular simple harmonic motion of the same frequency and unequal amplitude but differing in phase by `pi//2` is

Options

A. simple harmonic
B. circular
C. elliptical
D. parabolic

Answer

C

Explanation

If first equation is
`y_(1) = a_(1) sin omega t rArr sin t = (y_(1))/(a_(1))" "...(i)`
Then, second equation will be
`y_(2) = a_(2) sin (omega t + (pi)/(2))=a_(2) cos omega t`
`rArr" "cos omega t = (y_(2))/(a_(2))" "...(ii)`
By squaring and adding Eqs. (i) and (ii), we get
`sin^(2)omega t + cos^(2) omegat = (y_(1)^(2))/(a_(1)^(2))+(y_(2)^(2))/(a_(2)^(2))`
`rArr" "(y_(1)^(2))/(a_(1)^(2))+(y_(2)^(2))/(a_(2)^(2)) = 1`,
This is equation of an ellipse.