# 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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When the displacement is half the amplitude in an SHM, the ratio of potential energy to the total energy is:
1. 1 / 2

2. 1 / 4

3. 1

4. 1 / 8

Subtopic:  Energy of SHM |
81%
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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.

Subtopic:  Spring mass system |
59%
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A mass m is suspended from two springs of spring constant ${k}_{1}$ $and$ ${k}_{2}$ as shown in the figure below. The time period of vertical oscillations of the mass will be

1. $2\mathrm{\pi }\sqrt{\left(\frac{{\mathrm{k}}_{1}+{\mathrm{k}}_{2}}{\mathrm{m}}\right)}$

2. $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{\left({\mathrm{k}}_{1}+{\mathrm{k}}_{2}\right)}}$

3. $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}\left({\mathrm{k}}_{1}{\mathrm{k}}_{2}\right)}{\left({\mathrm{k}}_{1}+{\mathrm{k}}_{2}\right)}}$

4. $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}\left({\mathrm{k}}_{1}+{\mathrm{k}}_{2}\right)}{\left({\mathrm{k}}_{1}{\mathrm{k}}_{2}\right)}}$

Subtopic:  Combination of Springs |
77%
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In simple harmonic motion, the ratio of acceleration of the particle to its displacement at any time is a measure of:

 1 Spring constant 2 Angular frequency 3 (Angular frequency)2 4 Restoring force
Subtopic:  Simple Harmonic Motion |
81%
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The amplitude and the time period in an S.H.M. are 0.5 cm and 0.4 sec respectively. If the initial phase is $\mathrm{\pi }/2$ radian, then the equation of S.H.M. will be:

1. $\mathrm{y}=0.5\mathrm{sin}5\mathrm{\pi t}$

2. $\mathrm{y}=0.5\mathrm{sin}4\mathrm{\pi t}$

3. $\mathrm{y}=0.5\mathrm{sin}2.5\mathrm{\pi t}$

4. $\mathrm{y}=0.5\mathrm{cos}5\mathrm{\pi t}$

Subtopic:  Linear SHM |
69%
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The angular velocities of three bodies in simple harmonic motion are ${\omega }_{1},$ ${\omega }_{2},$ ${\omega }_{3}$ with their respective amplitudes as ${A}_{1},$ ${A}_{2},$ ${A}_{3}$. If all the three bodies have the same mass and maximum velocity, then:

 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 $$A_1^2 \omega_1^2=A_2^2 \omega_2^2=A^2$$
Subtopic:  Simple Harmonic Motion |
90%
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The total energy of a particle, executing simple harmonic motion is:

1. $\propto$ $x$

2. $\propto$ ${x}^{2}$

3.  Independent of x

4.  $\propto$ ${x}^{1/2}$

Subtopic:  Energy of SHM |
74%
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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

Subtopic:  Energy of SHM |
55%
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The equation of motion of a particle is $${d^2y \over dt^2}+Ky=0$$ where $$K$$ is a positive constant. The time period of the motion is given by:

 1 $$2 \pi \over K$$ 2 $$2 \pi K$$ 3 $$2 \pi \over \sqrt{K}$$ 4 $$2 \pi \sqrt{K}$$
Subtopic:  Simple Harmonic Motion |
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