The motion of a particle varies with time according to the relation y =a sin ωt+a cos ωt. Then:

1. The motion is oscillatory but not SHM
2. The motion is SHM with an amplitude \(a\sqrt{2}\)
3. The motion is SHM with an amplitude \(\sqrt{2}\) 
4. The motion is SHM with an amplitude \(a\)

Subtopic:  Simple Harmonic Motion |
 72%
From NCERT
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If a particle is executing SHM, with an amplitude A, the distance moved and the displacement of the body in a time equal to its time period are, respectively:

1. 2A, A 2. 4A, 0
3. A, A 4. 0, 2A
Subtopic:  Linear SHM |
 83%
From NCERT
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A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude?

(1) 12s

(2) 16s

(3) 14s

(4) 13s

Subtopic:  Simple Harmonic Motion |
 76%
From NCERT
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The uniform stick of mass m length L is pivoted at the centre. In the equilibrium position shown in the figure, the identical light springs have their natural length. If the stick is turned through a small angle θ, it executes SHM. The frequency of the motion is:

(1) 12π6Km

(2) 12π3K2m

(3) 12π3Km

(4) None of these

Subtopic:  Angular SHM |
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If the displacement x and the velocity v of a particle executing simple harmonic motion are related through the expression 4v2=25-x2,then its time period will be:

1. \(\pi \) 2. \(2 \pi \)
3. \(4 \pi \) 4. \(6 \pi\)
Subtopic:  Linear SHM |
 65%
From NCERT
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Two simple pendulums have time periods T and 5T4. They start vibrating at the same instant from the mean position in the same phase. The phase difference between them when bigger pendulum completes one oscillation will be:

1. π6

2. π4

3. π3

4. π2

Subtopic:  Simple Harmonic Motion |
 61%
From NCERT
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A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector a is correctly shown in: 

1.     2.
3. 4.
Subtopic:  Angular SHM |
From NCERT
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A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resulting amplitude is equal to the amplitude of individual motions, the phase difference between them will be:

1.  π3

2.  2π3

3.  π6

4.  π2

Subtopic:  Linear SHM |
 61%
From NCERT
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The variation of acceleration, \(a~\) of a particle executing SHM with displacement \(x~\) is:

1.     2.  
3.    4.   
Subtopic:  Simple Harmonic Motion |
 67%
From NCERT
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A second's pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket:

(1) Comes down with uniform acceleration

(2) Moves around the earth in a geostationary orbit

(3) Moves up with a uniform velocity

(4) Moves up with the uniform acceleration

Subtopic:  Simple Harmonic Motion |
 60%
From NCERT
PMT - 1994
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