A particle undergoes SHM with an amplitude of \(10\) cm and a time period of \(4\) s. The average velocity of the particle during the course of its motion from its mean position to its extreme position is:
1. \(5\) cm/s
2. \(10\) cm/s
3. at least \(10\) cm/s
4. at most \(10\) cm/s
Subtopic:  Simple Harmonic Motion |
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Two SHMs of the form:
\(x=A+A\text{sin}\omega t\\ y=A-A\text{sin}\omega t\)
are superposed on a particle, along \(x\) and \(y\) directions. The resultant of these motions is:
1. circular motion
2. SHM along \(x\)-axis
3. SHM along \(y\)-axis
4. SHM, but along a direction other than \(x\) or \(y\)-axis
Subtopic:  Simple Harmonic Motion |
 54%
From NCERT
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A particle executes SHM along a straight line.
Statement I: A graph of its acceleration vs displacement (from mean position) is a straight line.
Statement II: A graph of its velocity vs displacement (from mean position) is an ellipse.
 
1. Statement I is incorrect and Statement II is correct.
2. Both Statement I and Statement II are correct.
3. Both Statement I and Statement II are incorrect.
4. Statement I is correct and Statement II is incorrect.
Subtopic:  Simple Harmonic Motion |
 75%
From NCERT
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The maximum speed and acceleration of a particle undergoing SHM are \(v_0\) and \(a_0,\) respectively. The time period of the SHM is:
1. \(\dfrac{2\pi v_0}{a_0}\)

2. \(\dfrac{2\pi a_0}{v_0}\)

3. \(\dfrac{v_0}{a_0}\)

4. \(\dfrac{2v_0}{a_0}\)

Subtopic:  Simple Harmonic Motion |
 80%
From NCERT
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If the time of mean position from amplitude (extreme) position is \(6\) seconds, then the frequency of SHM will be:
1. \(0.01~\text{Hz}\) 2. \(0.02~\text{Hz}\)
3. \(0.03~\text{Hz}\) 4. \(0.04~\text{Hz}\)
Subtopic:  Simple Harmonic Motion |
 70%
From NCERT
AIPMT - 1998
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The time period of a particle in simple harmonic motion is equal to the time between consecutive appearances of the particle at a particular point in its motion. This point is:

1. the mean position
2. an extreme position
3. between the mean position and the positive extreme
4. between the mean position and the negative extreme
Subtopic:  Simple Harmonic Motion |
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A particle moves in a plane such that its displacements are the sum of two displacements \(\vec{ r}_1\), and \(\vec{r}_2;\) each of which undergo SHM in opposite phase with respect to the other, but of unequal amplitude. The resultant motion of the particle is:
1. uniform circular motion 
2. elliptical motion
3. linear SHM
4. angular SHM along a circle
Subtopic:  Simple Harmonic Motion |
From NCERT
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Two pendulums suspended from the same point have lengths of \(2\) m and \(0.5\) m. If they are displaced slightly and released, then they will be in the same phase when the small pendulum has completed:
1. \(2\) oscillations
2. \(4\) oscillations
3. \(3\) oscillations
4. \(5\) oscillations

Subtopic:  Simple Harmonic Motion |
 68%
From NCERT
AIPMT - 1998
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