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 omega t = (y_(1))/(a_(1))`
then second equation will be
`y_(2) = a_(2) sin (sin omega t cos (pi)/(2))`
`= a_(2)[sin omega t cos "(pi)/(2)+ cos omega t sin"(pi)/(2)]= a_(2) cos omega t `
`rArr cos omega t = (y_(2))/(a_(2))`
By squiring and adding (i) and (ii)
`sin ^(2) omega t + cos^(2) omega t = (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 the equation of ellipse