Question

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

A. the two S.H.M will cancel each other
B. the resulting motion is a linear simple harmonic motion along a straight line inclined equally to the straight lines of motion of the component ones
C. the resulting motion is an elliptical motion, symmetrical about the lines of motion of the components
D. none of these

Answer 1

When two mutually perpendicular simple harmonic motions of the same frequency, amplitude, and phase are combined, they result in an elliptical motion symmetrical about the components' motion lines. Option c is the answer.

Step-by-step explanation:

When two mutually perpendicular simple harmonic motions of the same frequency, amplitude, and phase are superimposed, the resulting motion is an elliptical motion, symmetrical about the lines of motion of the components (Option C). This is because each motion can be thought of as a projection of uniform circular motion onto its respective axis. When these motions are combined, the result is a projection of a point traveling in a circular path onto a two-dimensional plane, which creates an ellipse. If the amplitudes and frequencies are identical, and the phases are synchronized, this ellipse becomes a circle.