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
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 |
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. |
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 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. | \(3.2~\text{s}^{-1}\) |
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 |
A particle is executing SHM with time period T. If the time period of its total mechanical energy is T', then will be:
1. | 2 | 2. | \(1 \over 2\) |
3. | Zero | 4. | Infinite |
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. |
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. | \(\text{A} \over 2\) |
The displacement-time graph of a particle executing SHM is shown in the figure. Its displacement equation will be: (Time period = 2 second)
1.
2.
3.
4.