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 |
 83%
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A particle of mass \(m\) and charge \(\text-q\) moves diametrically through a uniformly charged sphere of radius \(R\) with total charge \(Q\). The angular frequency of the particle's simple harmonic motion, if its amplitude \(<R\), is given by:
1. \(\sqrt{\dfrac{qQ}{4 \pi \varepsilon_0 ~mR} }\)
2. \(\sqrt{\dfrac{qQ}{4 \pi \varepsilon_0 ~mR^2} }\)
3. \(\sqrt{\dfrac{qQ}{4 \pi \varepsilon_0 ~mR^3}}\)
4. \( \sqrt{\dfrac{m}{4 \pi \varepsilon_0 ~qQ} }\)

Subtopic:  Linear SHM |
 57%
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The figure shows the circular motion of a particle. The radius of the circle, the period, the sense of revolution, and the initial position are indicated in the figure. The simple harmonic motion of the \(\mathrm{x\text-}\)projection of the radius vector of the rotating particle \(P\) will be:

                                     

1. \(x \left( t \right) = B\) \(\text{sin} \left(\dfrac{2 πt}{30}\right)\)

2. \(x \left( t \right) = B\) \(\text{cos} \left(\dfrac{πt}{15}\right)\)

3. \(x \left( t \right) = B\) \(\text{sin} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)\)

4. \(x \left( t \right) = B\) \(\text{cos} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)\)

Subtopic:  Simple Harmonic Motion | Phasor Diagram |
 51%
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Displacement versus time curve for a particle executing SHM is shown in the figure. Choose the correct statement/s.

1. Phase of the oscillator is the same at t =0 s and t = 2 s.
2. Phase of the oscillator is the same at t =2 s and t=6 s.
3. Phase of the oscillator is the same at t = 1 s and t=7 s.
4. Phase of the oscillator is the same at t=1 s and t=5 s.

1. 1, 2 and 4 2. 1 and 3
3. 2 and 4 4. 3 and 4
Subtopic:  Simple Harmonic Motion |
 72%
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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 T'T will be:

1. 2 2. \(1 \over 2\)
3. Zero 4. Infinite
Subtopic:  Energy of 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 |
 92%
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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 |
 72%
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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 |
 73%
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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 |
 62%
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From the given functions, identify the function which represents a periodic motion:

1. \(e^{\omega t}\) 2. \(\text{log}_e(\omega t)\)
3. \(\text{sin}\omega t+ \text{cos}\omega t\) 4. \(e^{-\omega t}\)

Subtopic:  Types of Motion |
 88%
From NCERT
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