A particle is acted simultaneously by mutually perpendicular simple harmonic motion `x = a cos omega t` and `y= a sin omega t`. The frequency of motion of the particle will be

Options

A. as ellipse
B. a parabola
C. a circle
D. a straight line

Answer

C

Explanation

Given `x = a cos omega t`…(i)
`y = a sin omega t`…(ii)
Squaring and adding Eqs (i) and (ii)
`rArr x^(2) + y^(2) = a^(2) [:' cos^(2) omegat + sin^(2) omega t = 1]`
This is the equation, of the circle
Clearly the locus is a circle of constant radius a.