Question

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

• A. the resulting motion is uniform circular motion.
• 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.
• C. the resulting motion is an elliptical motion, symmetrical about the lines of motion of the components.
• D. the two S.H.M. will cancel each other.

Answer 1

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.

$\text{Given:-}$ Two mutually perpendicular simple harmonic motions of same frequency, amplitude and phase

$\text{Explanation:-}$ let us Assume

$x=Asin(\omega t+\varphi )$

$y=Asin(\omega t+\varphi )$ (given in the question)

So, $x=y$

Straight line passing through (0,0) and is inclined at ${45}^{\circ }$

$\text{Hence the correct option is B}$