# A particle executing SHM crosses points A and B with the same velocity. Having taken 3 s in passing from A to B, it returns to B after another 3 s. The time period of the SHM will be: 1. 15 s 2. 6 s 3. 12 s 4. 9 s

Subtopic:  Linear SHM |
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Which of the following examples represent simple harmonic motion?

 1 The rotation of the earth about its axis. 2 The motion of an oscillating mercury column in a U-tube. 3 General vibrations of a polyatomic molecule about its equilibrium position. 4 A fan rotating with a constant angular velocity.
Subtopic:  Simple Harmonic Motion |
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Which of the following relationships between the acceleration '$$a$$' and the displacement '$$x$$' of a particle involves simple harmonic motion?
1. $$a = 0 . 7 x$$
2. $$a = - 200 x^{2}$$
3. $$a = - 10 x$$
4. $$a = 100 x^{3}$$

Subtopic:  Simple Harmonic Motion |
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A spring having a spring constant of $$1200$$ N/m is mounted on a horizontal table as shown in the figure. A mass of $$3$$ kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of $$2.0$$ cm and released. The frequency of oscillations will be:

 1 $$3.0~\text{s}^{-1}$$ 2 $$2.7~\text{s}^{-1}$$ 3 $$1.2~\text{s}^{-1}$$ 4 $$3.2~\text{s}^{-1}$$
Subtopic:  Spring mass system |
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In a simple harmonic oscillation, the graph of acceleration against displacement for one complete oscillation will be:
1. an ellipse
2. a circle
3. a parabola
4. a straight line

Subtopic:  Linear SHM |
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Identify the correct definition:

 1 If after every certain interval of time, a particle repeats its motion, then the motion is called periodic motion. 2 To and fro motion of a particle is called oscillatory motion. 3 Oscillatory motion described in terms of single sine and cosine functions is called simple harmonic motion. 4 All of the above

Subtopic:  Types of Motion |
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A particle is executing SHM with time period T. If the time period of its total mechanical energy is T', then $\frac{{T}^{\text{'}}}{T}$ will be:

 1 2 2 $$1 \over 2$$ 3 Zero 4 Infinite
Subtopic:  Energy of SHM |
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The rotation of the earth about its axis is:

 1 periodic motion. 2 simple harmonic motion. 3 periodic and simple harmonic motion. 4 non-periodic motion.
Subtopic:  Types of Motion |
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All the surfaces are smooth and the system, given below, is oscillating with an amplitude $$\mathrm{A}.$$ What is the extension of spring having spring constant $$\mathrm{k_1},$$ when the block is at the extreme position?

 1 $${k_1 \over k_1+k_2} \text{A}$$ 2 $${k_2A \over k_1+k_2}$$ 3 $$\mathrm{A}$$ 4 $$\text{A} \over 2$$
Subtopic:  Combination of Springs |
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The displacement-time graph of a particle executing SHM is shown in the figure. Its displacement equation will be: (Time period = 2 second)

1. $\mathrm{x}=10$ $\mathrm{sin}\left(\mathrm{\pi t}+\frac{\mathrm{\pi }}{6}\right)$

2. $\mathrm{x}=10$ $\mathrm{sin}\left(\mathrm{\pi t}\right)$

3. $\mathrm{x}=10$ $\mathrm{cos}\left(\mathrm{\pi t}\right)$

4. $x=5$ $\mathrm{sin}\left(\mathrm{\pi t}+\frac{\mathrm{\pi }}{6}\right)$

Subtopic:  Linear SHM |
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