Q. No.When the displacement is half the amplitude in an SHM, the ratio of potential energy to the total energy is:
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. |
A mass m is suspended from two springs of spring constant as shown in the figure below. The time period of vertical oscillations of the mass will be
1.
2.
3.
4.
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. | Spring constant | 2. | Angular frequency |
| 3. | (Angular frequency)2 | 4. | Restoring force |
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. | \(A_1 \omega_1=A_2 \omega_2=A_3 \omega_3\) |
| 2. | \(A_1 \omega_1^2=A_2 \omega_2^2=A_3 \omega_3^2\) |
| 3. | \(A_1^2 \omega_1=A_2^2 \omega_2=A_3^2 \omega_3\) |
| 4. | \(A_1^2 \omega_1^2=A_2^2 \omega_2^2=A^2\) |
1. \(\propto x\)
2. \(\propto x^2\)
3. Independent of \(x\)
4. \(\propto x^{\frac{1}{2}}\)
A body is executing simple harmonic motion. At a displacement \(x,\) its potential energy is \(E_1\) and at a displacement \(y\), its potential energy is \(E_2\). The potential energy \(E\) at displacement \(x+y\) will be?
1. \(E = \sqrt{E_1}+\sqrt{E_2}\)
2. \(\sqrt{E} = \sqrt{E_1}+\sqrt{E_2}\)
3. \(E =E_1 +E_2\)
4. None of the above
| 1. | \(2 \pi \over K\) | 2. | \(2 \pi K\) |
| 3. | \(2 \pi \over \sqrt{K}\) | 4. | \(2 \pi \sqrt{K}\) |
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