# 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 |
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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 |
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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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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 |
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Kinetic energy of a particle executing simple harmonic motion in straight line is $$pv^2$$ and potential energy is $$qx^2,$$ where $$v$$ is speed at distance $$x$$ from the mean position. The time period of the SHM is given by the expression:

1. $2\mathrm{\pi }\sqrt{\frac{\mathrm{q}}{\mathrm{p}}}$

2. $2\mathrm{\pi }\sqrt{\frac{p}{q}}$

3. $2\mathrm{\pi }\sqrt{\frac{\mathrm{q}}{\mathrm{p}+\mathrm{q}}}$

4. $2\mathrm{\pi }\sqrt{\frac{p}{p+q}}$

Subtopic:  Energy of SHM |
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A simple pendulum of mass m swings about point B between extreme positions A and C. Net force acting on the bob at these three points is correctly shown by:

 1 2 3 4
Subtopic:  Angular SHM |
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The potential energy of a particle oscillating along the x-axis is given as U = 20+ (x–2)2 where U is in joules and x in meters. The total mechanical energy of the particle is 36 J. The maximum kinetic energy of the particle will be:
1. 24 J

2. 36 J

3. 16 J

4. 20 J

Subtopic:  Energy of SHM |
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A particle is executing SHM according to y = a cos$\mathrm{\omega t}$. Then, which of the following graphs represent variations of potential energy?

1. I and III

2. II and IV

3. II and III

4. I and IV

Subtopic:  Energy of SHM |
59%
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