Q. No.Which of the following examples represent periodic motion?
| 1. | A swimmer completing one (return) trip from one bank of a river to the other and back. |
| 2. | A freely suspended bar magnet displaced from its N-S direction and released. |
| 3. | Swaying of the branches of the tree. |
| 4. | An arrow released from a bow. |
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. |
The figure depicts four \((\mathrm{x-t})\) plots for the linear motion of a particle.
| (a) |  |
| (b) |  |
| (c) |  |
| (d) |  |
Which of the following is true?
| 1. | (a) is periodic but (c) is not periodic. |
| 2. | (b) is periodic but (d) is not periodic. |
| 3. | (b) and (d) are periodic. |
| 4. | only (c) is periodic. |
1. \(\frac{\pi}{\omega}\)
2. \(\frac{4 \pi}{\omega}\)
3. \(\frac{3 \pi}{\omega}\)
4. \(\frac{2 \pi}{\omega}\)
:
| 1. | a simple harmonic function. |
| 2. | a simple harmonic function but not a periodic function. |
| 3. | both periodic and simple harmonic function. |
| 4. | only periodic function. |
A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. (Take the direction from A to B as the positive direction.) The signs of velocity, acceleration, and force on the particle when it is at 3 cm away from A going towards B are:
1. Zero, Negative, Negative
2. Negative, Zero, Zero
3. Negative, Negative, Negative
4. Positive, Positive, Positive
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. | \(a = 100 x^{3}\) |
A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?
1. 219 N
2. 196 N
3. 223 N
4. 225 N
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. | \(3.2~\text{s}^{-1}\) |
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 maximum acceleration of the mass is:
1. \(6\) ms-2
2. \(8\) ms-2
3. \(3.3\) ms-2
4. \(5.1\) ms-2
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