A particle moves in a circular path with a continuously increasing speed. Its motion is:
1. periodic
2. oscillatory
3. simple harmonic
4. none of them

Subtopic:  Types of Motion |
 52%
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Identify the function which represents a non-periodic motion?
1. \(e^{-\omega t}\) 2. \(\text{sin}\omega t\)
3. \(\text{sin}\omega t+\text{cos}\omega t\) 4. \(\text{sin}(\omega t+\pi/4)\)
Subtopic:  Types of Motion |
 79%
From NCERT
NEET - 2022
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Trains travel between station A and station B: on the way up (from A to B) - they travel at a speed of \(80\) km/h, while on the return trip the trains travel at twice that speed. The services are maintained round the clock. Trains leave station A every \(30\) min for station B and reach B in \(2\) hrs. All trains operate continuously, without any rest at A or B.

1. the frequency of trains leaving B must be twice as much as A.
2. the frequency of trains leaving B must be half as much as A.
3. the frequency of trains leaving B is equal to that at A
4. the situation is impossible to maintain unless larger number of trains are provided at A.
Subtopic:  Types of Motion |
From NCERT
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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
Subtopic:  Simple Harmonic Motion |
From NCERT
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Two SHMs of the form:
\(x=A+Asin\omega t\\ y=A-Asin\omega t\)
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%
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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 |
 74%
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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. \(\frac{2\pi v_0}{a_0}\)

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

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

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

Subtopic:  Simple Harmonic Motion |
 79%
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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. \(0.01\) Hz 2. \(0.02\) Hz
3. \(0.03\) Hz 4. \(0.04\) Hz
Subtopic:  Simple Harmonic Motion |
 68%
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 \(\overrightarrow {r_1}\) , and \(\overrightarrow {r_2};\) 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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