A particle is attached to a vertical spring and pulled down a distance of 0.01 m below its mean position and released. If its initial acceleration is 0.16 $\mathrm{m}/{\mathrm{s}}^{2}$, then its time period in seconds will be:

1.  $\mathrm{\pi }$

2.  $\frac{\mathrm{\pi }}{2}$

3.  $\frac{\mathrm{\pi }}{4}$

4.  $2\mathrm{\pi }$

Subtopic:  Spring mass system |
88%
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The time period of the spring-mass system depends upon:

 1 the gravity of the earth 2 the mass of the block 3 spring constant 4 both (2) & (3)
Subtopic:  Spring mass system |
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The time periods for the figures (a) and (b) are ${\mathrm{T}}_{1}$ $\mathrm{and}$ ${\mathrm{T}}_{2}$ respectively. If all surfaces shown below are smooth, then the ratio $\frac{{\mathrm{T}}_{1}}{{\mathrm{T}}_{2}}$ will be:

1.  1: $\sqrt{3}$

2.  1: 1

3.  2: 1

4.  $\sqrt{3}$: 2

Subtopic:  Spring mass system |
81%
From NCERT
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The frequency of a spring is $$n$$ after suspending mass $$M.$$ Now, after mass $$4M$$ mass is suspended from the spring, the frequency will be:

 1 $$2n$$ 2 $$n/2$$ 3 $$n$$ 4 none of the above

Subtopic:  Spring mass system |
80%
From NCERT
AIPMT - 1998
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The period of oscillation of a mass M suspended from a spring of negligible mass is T. If along with it, another mass M is also suspended, the period of oscillation will now be:

1. T

2. T/$\sqrt{2}$

3. 2T

4. $\sqrt{2}$T

Subtopic:  Spring mass system |
78%
From NCERT
AIPMT - 2010
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One end of a spring of force constant $$\mathrm{k}$$ is fixed to a vertical wall and the other to a block of mass $$\mathrm{m}$$ resting on a smooth horizontal surface. There is another wall at a distance ${\mathrm{x}}_{0}$ from the block. The spring is then compressed by $2{\mathrm{x}}_{0}$ and then released. The time taken to strike the wall will be?

 1 $${1 \over 6} \pi \sqrt{ {k \over m}}$$ 2 $$\sqrt{ {k \over m}}$$ 3 $${2 \pi \over 3} \sqrt{ {m \over k}}$$ 4 $${ \pi \over 4} \sqrt{ {k \over m}}$$
Subtopic:  Spring mass system |
72%
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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 $$3.2~\text{s}^{-1}$$
Subtopic:  Spring mass system |
72%
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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. T/4
2. T
3. T/2
4. 2T

Subtopic:  Spring mass system |
72%
From NCERT
AIPMT - 2003
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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. $$2 \pi \sqrt{\frac{Ml}{\left(\right. m + M \left.\right) g}}$$

Subtopic:  Spring mass system |
59%
From NCERT
AIPMT - 1999
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An ideal spring with spring-constant K is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially un-stretched. Then the maximum extension in the spring will be:
1. 4 Mg/K
2. 2 Mg/K
3. Mg/K
4. Mg/2K

Subtopic:  Spring mass system |
56%
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