Out of the statements given, which is/are correct ?

Engineering

Physics

Superposition of Simple Harmonic Motion

Basics of Simple Harmonic Motion

Question

Out of the statements given, which is/are correct ?

A

The amplitude of a resultant simple harmonic motion obtained by superposition of two simple harmonic motions along the same direction can be less than lesser of the amplitudes of the participating SHMs.

B

When two simple harmonic motions which are in phase and in perpendicular directions superpose then resulting motion will be SHM with same phase.

C

The combination of two simple harmonic motions of equal amplitude in perpendicular directions differing in phase by π/2 rad is a circular motion.

D

When two simple harmonic motions (with amplitudes A₁ and A₂) which are out of phase (that means phase difference p) and in perpendicular directions, superpose then resulting motion will be SHM with amplitude $\sqrt{A_{1}^{2} + A_{2}^{2}}$ .

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A is correct as

$A_{r}^{2} = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cosφ} = \sqrt{{(A_{1} - A_{2})}^{2} - 2 A_{1} A_{2} (1 - cosφ)}$

B & C are correct as

$R = \sqrt{x^{2} + y^{2}} = \sqrt{A_{1}^{2} + A_{2}^{2}} \sin (ωt + φ)$

D is correct as x = A sin (ωt + φ),

y = a cos (ωt + φ)

x² + y² = A² is an equation of circular motion.