Two simple harmonic motions act on a particle. These harmonic motions are $x = A\cos{(\omega t + \delta);A\cos{(\omega t + \alpha)\ when\ }}$

Question

Dr. Abubacker · Accepted Answer

(c) $x = A\cos\left( \omega t + \alpha + \frac{\pi}{2} \right)$
$= - A\sin{(\omega t + \alpha)}$ …(i)
$Y = A\cos{(\omega t + \alpha)}$ …(ii)
Squaring and adding Eqs. (i) and (ii), we get
$x^{2} + y^{2} = A^{2}\left\lbrack \sin^{2}(\omega t + \alpha) + \cos^{2}(\omega t + \alpha) \right\rbrack = A^{2}$
It is an equation of a circle. The given motion is anticlockwise

Q. Two simple harmonic motions act on a particle. These harmonic motions are $x = A\cos{(\omega t + \delta);A\cos{(\omega t + \alpha)\ when\ }}$

Explanation

Reviewed by Dr. Abubacker

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