When two mutually perpendicular simple harmonic motions of same frequency, amplitude and phase are superimposed

The resulting motion is uniform circular motion.

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The resulting motion is a linear simple harmonic motion along a straight line inclined equally to the straight lines of motion of component ones.

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The resulting motion is an elliptical motion, symmetrical about the lines of motion of the components.

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The two S.H.M's will cancel each other.

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Solution

The correct option is B
The resulting motion is a linear simple harmonic motion along a straight line inclined equally to the straight lines of motion of component ones.

$Y_{1} = A_{1} s i n w t; y_{2} = A_{2} s i n (w t + \frac{π}{2})$

$A^{2} = \sqrt{A_{1}^{2} + A_{2}^{2}}$ $θ = t a n^{- 1} (\frac{A_{2}}{A_{1}})$

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When two mutually perpendicular simple harmonic motions of same frequency, amplitude and phase are superimposed

The correct option is B The resulting motion is a linear simple harmonic motion along a straight line inclined equally to the straight lines of motion of component ones. Y1=A1 sin wt;y2=A2 sin(wt+π2) A2=√A21+A22 θ=tan−1(A2A1)