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. |
| 1. | The rotation of the earth about its axis. |
| 2. | The motion of an oscillating mercury column in a \(U\text-\)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 \((\mathrm{x\text-t})\) 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 functions. |
| 4. | only periodic function. |
A particle is in linear simple harmonic motion between two points, \(A\) and \(B\), \(10~\text{cm}\) 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 \(3~\text{cm}\) 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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