Q. No.Kinetic energy of a particle executing simple harmonic motion in straight line is \(pv^2\) and potential energy is \(qx^2,\) where \(v\) is speed at distance \(x\) from the mean position. The time period of the SHM is given by the expression:
1. \(2\pi \sqrt{\frac{q}{p}}\)
2. \(2\pi \sqrt{\frac{p}{q}}\)
3. \(2\pi \sqrt{\frac{q}{p+q}}\)
4. \(2\pi \sqrt{\frac{p}{p+q}}\)
1. \(y = 0.5\sin(5\pi t)\)
2. \(y = 0.5\sin(4\pi t)\)
3. \(y = 0.5\sin(2.5\pi t)\)
4. \(y = 0.5\cos(5\pi t)\)
| 1. | Spring constant | 2. | Angular frequency |
| 3. | (Angular frequency)2 | 4. | Restoring force |
One end of a spring of force constant \(k\) is fixed to a vertical wall and the other to a block of mass \(m\) resting on a smooth horizontal surface. There is another wall at a distance \(x_0\) from the block. The spring is then compressed by \(2x_0\)
| 1. | \(\frac{1}{6} \pi \sqrt{ \frac{k}{m}}\) | 2. | \( \sqrt{\frac{k}{m}}\) |
| 3. | \(\frac{2\pi}{3} \sqrt{ \frac{m}{k}}\) | 4. | \(\frac{\pi}{4} \sqrt{ \frac{k}{m}}\) |
1. \(\frac{1}{2}\)
2. \(\frac{1}{4}\)
3. \(1\)
4. \(\frac{1}{8}\)
A block is connected to a relaxed spring and kept on a smooth floor. The block is given a velocity towards the right. Just after this:
| 1. | the speed of block starts decreasing but acceleration starts increasing. |
| 2. | the speed of the block as well as its acceleration starts decreasing. |
| 3. | the speed of the block starts increasing but its acceleration starts decreasing. |
| 4. | the speed of the block as well as acceleration start increasing. |
1. \(24~\text{J}\)
2. \(36~\text{J}\)
3. \(16~\text{J}\)
4. \(20~\text{J}\)
Two springs, of force constants k1 and k2 are connected to a mass m as shown in the figure. The frequency of oscillation of the mass is f. If both k1 and k2 are made four times their original values, the frequency of oscillation will become:
| 1. | 2f | 2. | f/2 |
| 3. | f/4 | 4. | 4f |
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