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 |
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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 |
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Trains travel between station \(A\) and station \(B\): on the way up (from \(A~\text{to}~B\)) - 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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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