Q. No.A mass is connected to a spring and it vibrates up and down, forming a simple harmonic system. Which of the following is/are correct?
| (a) | The kinetic energy of the mass is at a maximum halfway up. |
| (b) | The potential energy of the system is at a maximum at the top of the mass's motion. |
| (c) | The potential energy of the system is at a maximum at the bottom of the mass's motion. |
Choose the correct option from the given ones:
| 1. | (a), (b) and (c) | 2. | (a) and (b) only |
| 3. | (b) only | 4. | (c) only |
1. \(\pi\)
2. \(\frac{\pi}{2}\)
3. \(\frac{\pi}{4}\)
4. \(2\pi\)
| 1. | the gravity of the earth | 2. | the mass of the block |
| 3. | spring constant | 4. | both (2) & (3) |
1. \(1:\sqrt{3}\)
2. \(1:1\)
3. \(2:1\)
4. \(\sqrt{3}:2\)
| 1. | \(2n\) | 2. | \(n/2\) |
| 3. | \(n\) | 4. | none of the above |
1. \(T\)
2. \(\frac{T}{\sqrt{2}}\)
3. \(2T\)
4. \(\sqrt{2}T\)
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. | \(\frac{\pi}{4} \sqrt{ \frac{k}{m}}\) |
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. | \(3.2~\text{s}^{-1}\) |
The time period of a mass suspended from a spring is \(T\). If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be:
1. \(\frac{T}{4}\)
2. \(T\)
3. \(\frac{T}{2}\)
4. \(2T\)
A spring elongates by a length 'L' when a mass 'M' is suspended to it. Now a tiny mass 'm' is attached to the mass 'M' and then released. The new time period of oscillation will be:
1. \(2 \pi \sqrt{\frac{\left(\right. M + m \left.\right) l}{Mg}}\)
2. \(2 \pi \sqrt{\frac{ml}{Mg}}\)
3. \(2 \pi \sqrt{L / g}\)
4. \(2 \pi \sqrt{\frac{Ml}{\left(\right. m + M \left.\right) g}}\)
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