Q. No.The displacement-time graph of a particle executing SHM is shown in the figure. Its displacement equation will be: (Time period = \(2\) second)
1. \(x= 10\sin\left(\pi t+\frac{\pi}{6}\right)\)
2. \(x= 10\sin\left(\pi t\right)\)
3. \(x= 10\cos\left(\pi t\right)\)
4. \(x= 5\sin\left(\pi t+\frac{\pi}{6}\right)\)
1. \(x= 10\sin\left(\pi t+\frac{\pi}{6}\right)\)
2. \(x= 10\sin\left(\pi t\right)\)
3. \(x= 10\cos\left(\pi t\right)\)
4. \(x= 5\sin\left(\pi t+\frac{\pi}{6}\right)\)
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. | \(\text{A} \over 2\) |
A spring is having a spring constant k. It is cut into two parts A and B whose lengths are in the ratio of m:1. The spring constant of part A will be
1.
2.
3. k
4.
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
\(B\), it returns to \(B\) after another \(3~\text{s}\). The time period of the SHM will be:
| 1. | \(15~\text{s}\) | 2. | \(6~\text{s}\) |
| 3. | \(12~\text{s}\) | 4. | \(9~\text{s}\) |
| 1. | \(2v_0 \over \sqrt{3}\) | 2. | \(\sqrt{2}v_0 \over 3\) |
| 3. | \({2 \over 3}v_0\) | 4. | \(\sqrt{\frac{2}{3}}v_0\) |
| 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. |
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. | \(3.2~\text{s}^{-1}\) |
Acceleration of the particle at \(t = \frac{8}{3}~\text{s}\) from the given displacement \((y)\) versus time \((t)\) graph will be?
1. \(\frac{\sqrt{3}\pi^2}{4}~\text{cm/s}^2\)
2. \(-\frac{\sqrt{3}\pi^2}{4}~\text{cm/s}^2\)
3. \(-\pi^2~\text{cm/s}^2\)
4. zero
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