Question

A particle is subjected simultaneously to two simple harmonic motion of same period but of different amplitudes and phases in perpendicular direction. Find the expression for the resultant motion. For what condition path may be straight line.​

Answer 1

The first statement is wrong because two SHM's can be superimposed at an angle instead of having the same amplitude and frequency. But, if it is superimposed in opposite direction its resultant becomes zero.

The second statement is a true statement because for perpendicular superimposition.

Consider a wave,

x=A0cosω0t

then, y=Acos(ω0t+2π)

On superimpositon,

x2+y2=A2cos2ω0t+A2sin2ω0t

x2+y2=A2

This proves that the particle will perform circular motion.