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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
1. \(5\) cm/s
2. \(10\) cm/s
3. at least \(10\) cm/s
4. at most \(10\) cm/s
Subtopic: Â Simple Harmonic Motion |
Level 3: 35%-60%
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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:
\(x=A+A\text{sin}\omega t\\ y=A-A\text{sin}\omega t\)
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: Â Simple Harmonic Motion |
 54%
Level 3: 35%-60%
Hints
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: Â Simple Harmonic Motion |
 77%
Level 2: 60%+
Hints
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: Â Simple Harmonic Motion |
 80%
Level 1: 80%+
Hints
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: Â Simple Harmonic Motion |
 70%
Level 2: 60%+
AIPMT - 1998
Hints
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: Â Simple Harmonic Motion |
Level 3: 35%-60%
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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: Â Simple Harmonic Motion |
Level 3: 35%-60%
Hints
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: Â Simple Harmonic Motion |
 69%
Level 2: 60%+
AIPMT - 1998
Hints
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