A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motions, find the phase difference between the individual motions.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C

Let the amplitudes of the individual motions be A each. The resultant amplitude is also A. If the phase difference between the two motions is $δ$ ,

$A = \sqrt{A^{2} + A^{2} + 2 A . A . c o s δ}$

or, $A = A \sqrt{2 (1 + c o s δ)} = 2 A c o s \frac{δ}{2}$

or, $c o s \frac{δ}{2} = \frac{1}{2}$

or, $δ = \frac{2 π}{3}$

Suggest Corrections

Similar questions

Q. A particle is subjected to two simple harmonic motions of the same frequency and direction. The amplitude of the first motion is

4.0

c m

and that of the second is

3.0

c m

. Find resultant amplitude when the phage difference is

180^{0}

. Find the resultant amplitude if the phase difference between the two motions is

0^{\circ}

A particle is subjected to two simple harmonic motions of same time period in the same direction. The amplitude of the first motion is 3.0 cm and that of the second 4.0 cm. Find the resultant amplitude if the phase difference between the motions is (a) $0^{\circ},$ (b) $60^{\circ},$ (c) $90^{\circ} .$

Q. Assertion :A particle, simultaneously subjected to two simple harmonic motions of same frequency and same amplitude, will perform SHM only if the two SHM's are in the same direction. Reason: A particle, simultaneously subjected to two simple harmonic motions of same frequency and same amplitude, perpendicular to each other the particle will be in uniform circular motion.

Q. Three simple harmonic motions of equal amplitude A and equal time periods in the same direction combine. The phase of the second motion is 60° ahead of the first and the phase of the third motion is 60° ahead of the second. Find the amplitude of the resultant motion.

Two linear simple harmonic motions of equal amplitude and frequency are

impressed on a particle along x and y-axis respectively. The initial phase difference between them is

\frac{π}{2}

. The resultant path followed by the particle is :

Join BYJU'S Learning Program

A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motions, find the phase difference between the individual motions.

The correct option is C Let the amplitudes of the individual motions be A each. The resultant amplitude is also A. If the phase difference between the two motions is δ, A=√A2+A2+2A.A.cos δ or, A=A√2(1+cos δ)=2A cosδ2 or, cos δ2=12 or, δ=2π3