Q. No.A block of mass \(m\) is suspended from a massless spring with a spring constant of \(\dfrac{2 k}{3}\) as shown in the figure. When the block is slightly displaced vertically downward and released, it undergoes simple harmonic motion (SHM). The time period of the oscillation is given by:
| 1. | \(2 \pi \sqrt{\dfrac{m}{k}}\) | 2. | \(2 \pi \sqrt{\dfrac{m}{2k}}\) |
| 3. | \(2 \pi \sqrt{\dfrac{3m}{2k}}\) | 4. | \(2 \pi \sqrt{\dfrac{2m}{3k}}\) |
Subtopic: Spring mass system |
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A block of mass \(0.2~\text{kg}\) slides without friction on a \(30^{\circ}\) incline and is connected at the top by a massless spring of spring constant \(80~\text{N/m}\) as shown. If the block is pulled slightly down the incline and released, the time period of the ensuing motion is:
| 1. | \( \dfrac{\pi}{2} ~\text{s}\) | 2. | \( \dfrac{\pi}{5} ~\text{s}\) |
| 3. | \( \dfrac{\pi}{10}~\text{s}\) | 4. | \( \dfrac{\pi}{4}~\text{s}\) |
Subtopic: Spring mass system |
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Two springs, one of spring constant \(100~\text{Nm}^{-1}\) and the other of \(300~\text{Nm}^{-1}\) are joined vertically one above the other, and hung from support at the top. A mass of \(3~\text{kg}\) is attached to the lower spring. The time period of simple harmonic motion of such a system is:
| 1. | \(\dfrac{4\pi}{10}~\text{s}\) | 2. | \(\dfrac{3\pi}{10}~\text{s}\) |
| 3. | \(\dfrac{2\pi}{7}~\text{s}\) | 4. | \(\dfrac{\pi}{10}~\text{s}\) |
Subtopic: Spring mass system |
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A linear simple harmonic oscillator consists of a block with a mass of \(6~\text{kg}\) and a spring constant of \(600~\text{N}/\text{m}\) as shown in the figure. The surface is frictionless. What is the time period of oscillation of the system?
| 1. | \(10\) s | 2. | \(\dfrac{1}{10}\) s |
| 3. | \(0.63\) s | 4. | \(0.5\) s |
Subtopic: Spring mass system |
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A block, when suspended from a spring, causes it to extend by a length \(l,\) in equilibrium. If the block is attached to the same spring and allowed to oscillate the time period of oscillation will be:
| 1. | \(\begin{aligned}2\pi\sqrt{\large{\frac{l}{g}}} & \\ \end{aligned}\) | 2. | \(\begin{aligned}\pi\sqrt{\large{\frac{l}{g}}} & \\ \end{aligned}\) |
| 3. | \(\begin{aligned}2{\large\sqrt{\frac{l}{g}}} & \\ \end{aligned}\) | 4. | \(\begin{aligned} 2{\large\sqrt{\frac{g}{l}}} & \\ \end{aligned}\) |
Subtopic: Spring mass system |
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A spring having a spring constant of \(1200~\text{N/m}\) is mounted on a horizontal table. A mass of \(3~\text{kg}\) is attached to the free and of the spring. The mass is then pulled sideways to a distance of \(2~\text{cm}\) and released. The maximum speed of the mass is:
1. \(0.8~\text{m/s}\)
2. \(0.4~\text{m/s}\)
3. \(0.2~\text{m/s}\)
4. \(1.2~\text{m/s}\)
1. \(0.8~\text{m/s}\)
2. \(0.4~\text{m/s}\)
3. \(0.2~\text{m/s}\)
4. \(1.2~\text{m/s}\)
Subtopic: Spring mass system |
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A \(5\) kg collar is attached to a spring with a spring constant of \(500\) N/m. The collar slides over a horizontal rod without friction. The collar is displaced from its equilibrium position and released. Its period of oscillation will be:
| 1. | \(6.3~\text{s}\) | 2. | \(0.63~\text{s}\) |
| 3. | \(3.14~\text{s}\) | 4. | \(0.314~\text{s}\) |
Subtopic: Spring mass system |
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In figure (A), mass ‘2 m’ is fixed on mass ‘m’ which is attached to two springs of spring constant k. In figure (B), mass ‘m’ is attached to two spring of spring constant ‘k’ and ‘2k’. If mass ‘m’ in (A) and (B) are displaced by distance ‘x’ horizontally and then released, then time period T1 and T2 corresponding to (A) and (B) respectively follow the relation
1. \(\frac{T_{1}}{T_{2}}=\frac{3}{\sqrt{2}}\)
2. \(\frac{T_{1}}{T_{2}}=\sqrt{\frac{3}{2}} \)
3. \(\frac{T_{1}}{T_{2}}=\sqrt{\frac{2}{3}} \)
4. \(\frac{T_{1}}{T_{2}}=\frac{\sqrt{2}}{3}\)
1. \(\frac{T_{1}}{T_{2}}=\frac{3}{\sqrt{2}}\)
2. \(\frac{T_{1}}{T_{2}}=\sqrt{\frac{3}{2}} \)
3. \(\frac{T_{1}}{T_{2}}=\sqrt{\frac{2}{3}} \)
4. \(\frac{T_{1}}{T_{2}}=\frac{\sqrt{2}}{3}\)
Subtopic: Spring mass system |
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JEE
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A body of mass \(m\) is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass \(m\) is slightly pulled down and released, it oscillates with a time period of \(3~\text{s}\). When the mass \(m\) is increased by \(1~\text{kg}\), the time period of oscillations becomes \(5~\text{s}\). The value of \(m\) in \(\text{kg}\) is:
1. \(\dfrac{3}{4}\)
2. \(\dfrac{4}{3}\)
3. \(\dfrac{16}{9}\)
4. \(\dfrac{9}{16}\)
Subtopic: Spring mass system |
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NEET - 2016
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Two massless springs with spring constants \(2k\) and \(9k\), carry \(50~\text{g}\) and \(100~\text{g}\) masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be:
1. \(1:2\)
2. \(3:2\)
3. \(3:1\)
4. \(2:3\)
1. \(1:2\)
2. \(3:2\)
3. \(3:1\)
4. \(2:3\)
Subtopic: Spring mass system |
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JEE
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