Two particles are executing SHM about the same mean position, along the same straight line, with the same amplitude and time period. At any instant, they meet each other at, \(\frac{-A}{2}\) while moving in the opposite direction. The phase difference between them is:
1. \(\frac{2\pi}{3}\)
2. \(\frac{\pi}{3}\)
3. \(\frac{11\pi}{6}\)
4. \(\frac{7\pi}{6}\)

Subtopic:  Simple Harmonic Motion |
 65%
From NCERT
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A small block of mass m is kept on a wooden plank which is oscillating in the vertical plane (as shown), with time period T. The amplitude of oscillation at which block leaves contact with the plank is

                    

1.  gT24π

2.  gT24π

3.  gT24π2

4.  gT24π2

Subtopic:  Simple Harmonic Motion |
 66%
From NCERT
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A particle performing S.H.M. is at rest at points P and Q which are at a distance a and b from point O. It has velocity v when it is halfway between P and Q. The time period of oscillation is:

                

1.  b - ab×av

2.  πb - av

3.  b - abav

4.  Data is insufficient to answer.

Subtopic:  Simple Harmonic Motion |
 74%
From NCERT
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The time period of a simple pendulum in a stationary lift is T. If the lift moves upwards with an acceleration g, then the new time period will be

1.  Infinite

2.  0.6T

3.  1.67T

4.  0.707T

Subtopic:  Simple Harmonic Motion |
 71%
From NCERT
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Acceleration-time (\(a-t\)) graph for a particle performing S.H.M. is shown in the figure. Select the incorrect statement.

             
 

1. displacement of a particle at \(A\) is negative.
2. the potential energy of the particle at \(C\) is minimum.
3. the velocity of the particle at \(B\) is positive.
4. speed of particle at \(D\) is decreasing.

Subtopic:  Simple Harmonic Motion |
 57%
From NCERT
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A particle is executing S.H.M. such that its acceleration 'a' is a function of displacement x as a = -βx - 6. The time period of the oscillation is

1.  πβ

2.  π2β

3.  2π2β

4.  2πβ

Subtopic:  Simple Harmonic Motion |
 79%
From NCERT
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A particle of mass 0.5 kg is executing S.H.M. such that its potential energy is 5 J at the mean position. If its total mechanical energy is 9 J and the amplitude of oscillation is 1 cm, then the time period of oscillation of the particle is:

1.  2π100 s

2.  π200 s

3.  2π25 s

4.  2π s

Subtopic:  Energy of SHM |
 79%
From NCERT
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The total mechanical energy of a linear harmonic oscillator is \(600\) J. At the mean position, its potential energy is \(100\) J. The minimum potential energy of the oscillator is: 
1. \(50\) J
2. \(500\) J
3. \(0\) 
4. \(100\) J

Subtopic:  Energy of SHM |
 72%
From NCERT
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A general graph showing variation in the potential energy \((P.E)\) of a particle with time while executing S.H.M. is:

1. 2.
3. 4.
Subtopic:  Energy of SHM |
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Two simple pendulums of lengths 1.44 m and 1 m start S.H.M. together in the same phase. They will be in the same phase again after

1.  6 vibrations of the longer pendulum

2.  6 vibrations of the smaller pendulum

3.  5 vibrations of the smaller pendulum

4.  4 vibrations of the longer pendulum

Subtopic:  Angular SHM |
 71%
From NCERT
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