Super Position of SHM’s
PHXI14:OSCILLATIONS

364511 Three simple harmonic motions, of equal amplitudes \(A\) and equal time periods, along the same line combine. The phase of the second motion is \(60^{\circ}\) ahead of the first and phase of the third motion is \(60^{\circ}\) ahead of the second. The amplitude of resultant motion is ____.

1 \(\dfrac{A}{2}\)
2 \(\sqrt{3} A\)
3 \(2 \sqrt{2} A\)
4 \(2\;A\)
PHXI14:OSCILLATIONS

364512 The displacement \(x\) of a particle executing a certain periodic motion is given by \(y=25 \sin (4 t) \cos ^{2}(5 t)\). This expression may be considered to be the superposition of \(n\) independent harmonic motions. What is the value of \(n\) ?

1 2
2 3
3 4
4 5
PHXI14:OSCILLATIONS

364513 Two linear simple harmonic motions of equal amplitude and frequency are imposed on a particle along \(x\) and \(y\) axis respectively. The initial phase difference between them is \(\dfrac{\pi}{2}\). The resultant path followed by the particle is:

1 A circle
2 A straight line
3 An ellipse
4 A parabola
PHXI14:OSCILLATIONS

364514 A particle is executing two different simple harmonic motions, mutually perpendicular, of different amplitudes and having phase difference of \(\pi / 2\). The path of the particle will be

1 circular
2 straight line
3 parabolic
4 elliptical
PHXI14:OSCILLATIONS

364515 Two SHMs \(r_{1}=A \sin \omega t\) and \(r_{2}=B \sin \omega t\) are superposed on a particle. \(r_{1}\) and \(r_{2}\) are along the directions which make \(37^{0}\) with each other. Choose the correct statement

1 The particle will perform SHM.
2 The path of the particle is a circle
3 The particle will perform only periodic motion but not SHM
4 The path is a closed curve but not a straight line
PHXI14:OSCILLATIONS

364511 Three simple harmonic motions, of equal amplitudes \(A\) and equal time periods, along the same line combine. The phase of the second motion is \(60^{\circ}\) ahead of the first and phase of the third motion is \(60^{\circ}\) ahead of the second. The amplitude of resultant motion is ____.

1 \(\dfrac{A}{2}\)
2 \(\sqrt{3} A\)
3 \(2 \sqrt{2} A\)
4 \(2\;A\)
PHXI14:OSCILLATIONS

364512 The displacement \(x\) of a particle executing a certain periodic motion is given by \(y=25 \sin (4 t) \cos ^{2}(5 t)\). This expression may be considered to be the superposition of \(n\) independent harmonic motions. What is the value of \(n\) ?

1 2
2 3
3 4
4 5
PHXI14:OSCILLATIONS

364513 Two linear simple harmonic motions of equal amplitude and frequency are imposed on a particle along \(x\) and \(y\) axis respectively. The initial phase difference between them is \(\dfrac{\pi}{2}\). The resultant path followed by the particle is:

1 A circle
2 A straight line
3 An ellipse
4 A parabola
PHXI14:OSCILLATIONS

364514 A particle is executing two different simple harmonic motions, mutually perpendicular, of different amplitudes and having phase difference of \(\pi / 2\). The path of the particle will be

1 circular
2 straight line
3 parabolic
4 elliptical
PHXI14:OSCILLATIONS

364515 Two SHMs \(r_{1}=A \sin \omega t\) and \(r_{2}=B \sin \omega t\) are superposed on a particle. \(r_{1}\) and \(r_{2}\) are along the directions which make \(37^{0}\) with each other. Choose the correct statement

1 The particle will perform SHM.
2 The path of the particle is a circle
3 The particle will perform only periodic motion but not SHM
4 The path is a closed curve but not a straight line
PHXI14:OSCILLATIONS

364511 Three simple harmonic motions, of equal amplitudes \(A\) and equal time periods, along the same line combine. The phase of the second motion is \(60^{\circ}\) ahead of the first and phase of the third motion is \(60^{\circ}\) ahead of the second. The amplitude of resultant motion is ____.

1 \(\dfrac{A}{2}\)
2 \(\sqrt{3} A\)
3 \(2 \sqrt{2} A\)
4 \(2\;A\)
PHXI14:OSCILLATIONS

364512 The displacement \(x\) of a particle executing a certain periodic motion is given by \(y=25 \sin (4 t) \cos ^{2}(5 t)\). This expression may be considered to be the superposition of \(n\) independent harmonic motions. What is the value of \(n\) ?

1 2
2 3
3 4
4 5
PHXI14:OSCILLATIONS

364513 Two linear simple harmonic motions of equal amplitude and frequency are imposed on a particle along \(x\) and \(y\) axis respectively. The initial phase difference between them is \(\dfrac{\pi}{2}\). The resultant path followed by the particle is:

1 A circle
2 A straight line
3 An ellipse
4 A parabola
PHXI14:OSCILLATIONS

364514 A particle is executing two different simple harmonic motions, mutually perpendicular, of different amplitudes and having phase difference of \(\pi / 2\). The path of the particle will be

1 circular
2 straight line
3 parabolic
4 elliptical
PHXI14:OSCILLATIONS

364515 Two SHMs \(r_{1}=A \sin \omega t\) and \(r_{2}=B \sin \omega t\) are superposed on a particle. \(r_{1}\) and \(r_{2}\) are along the directions which make \(37^{0}\) with each other. Choose the correct statement

1 The particle will perform SHM.
2 The path of the particle is a circle
3 The particle will perform only periodic motion but not SHM
4 The path is a closed curve but not a straight line
PHXI14:OSCILLATIONS

364511 Three simple harmonic motions, of equal amplitudes \(A\) and equal time periods, along the same line combine. The phase of the second motion is \(60^{\circ}\) ahead of the first and phase of the third motion is \(60^{\circ}\) ahead of the second. The amplitude of resultant motion is ____.

1 \(\dfrac{A}{2}\)
2 \(\sqrt{3} A\)
3 \(2 \sqrt{2} A\)
4 \(2\;A\)
PHXI14:OSCILLATIONS

364512 The displacement \(x\) of a particle executing a certain periodic motion is given by \(y=25 \sin (4 t) \cos ^{2}(5 t)\). This expression may be considered to be the superposition of \(n\) independent harmonic motions. What is the value of \(n\) ?

1 2
2 3
3 4
4 5
PHXI14:OSCILLATIONS

364513 Two linear simple harmonic motions of equal amplitude and frequency are imposed on a particle along \(x\) and \(y\) axis respectively. The initial phase difference between them is \(\dfrac{\pi}{2}\). The resultant path followed by the particle is:

1 A circle
2 A straight line
3 An ellipse
4 A parabola
PHXI14:OSCILLATIONS

364514 A particle is executing two different simple harmonic motions, mutually perpendicular, of different amplitudes and having phase difference of \(\pi / 2\). The path of the particle will be

1 circular
2 straight line
3 parabolic
4 elliptical
PHXI14:OSCILLATIONS

364515 Two SHMs \(r_{1}=A \sin \omega t\) and \(r_{2}=B \sin \omega t\) are superposed on a particle. \(r_{1}\) and \(r_{2}\) are along the directions which make \(37^{0}\) with each other. Choose the correct statement

1 The particle will perform SHM.
2 The path of the particle is a circle
3 The particle will perform only periodic motion but not SHM
4 The path is a closed curve but not a straight line
PHXI14:OSCILLATIONS

364511 Three simple harmonic motions, of equal amplitudes \(A\) and equal time periods, along the same line combine. The phase of the second motion is \(60^{\circ}\) ahead of the first and phase of the third motion is \(60^{\circ}\) ahead of the second. The amplitude of resultant motion is ____.

1 \(\dfrac{A}{2}\)
2 \(\sqrt{3} A\)
3 \(2 \sqrt{2} A\)
4 \(2\;A\)
PHXI14:OSCILLATIONS

364512 The displacement \(x\) of a particle executing a certain periodic motion is given by \(y=25 \sin (4 t) \cos ^{2}(5 t)\). This expression may be considered to be the superposition of \(n\) independent harmonic motions. What is the value of \(n\) ?

1 2
2 3
3 4
4 5
PHXI14:OSCILLATIONS

364513 Two linear simple harmonic motions of equal amplitude and frequency are imposed on a particle along \(x\) and \(y\) axis respectively. The initial phase difference between them is \(\dfrac{\pi}{2}\). The resultant path followed by the particle is:

1 A circle
2 A straight line
3 An ellipse
4 A parabola
PHXI14:OSCILLATIONS

364514 A particle is executing two different simple harmonic motions, mutually perpendicular, of different amplitudes and having phase difference of \(\pi / 2\). The path of the particle will be

1 circular
2 straight line
3 parabolic
4 elliptical
PHXI14:OSCILLATIONS

364515 Two SHMs \(r_{1}=A \sin \omega t\) and \(r_{2}=B \sin \omega t\) are superposed on a particle. \(r_{1}\) and \(r_{2}\) are along the directions which make \(37^{0}\) with each other. Choose the correct statement

1 The particle will perform SHM.
2 The path of the particle is a circle
3 The particle will perform only periodic motion but not SHM
4 The path is a closed curve but not a straight line