# The radius of the circle, the period of revolution, initial position and direction of revolution are indicated in the figure.      The $$y$$-projection of the radius vector of rotating particle $$P$$ will be: 1. $$y(t)=3 \cos \left(\dfrac{\pi \mathrm{t}}{2}\right)$$, where $$y$$ in m 2. $$y(t)=-3 \cos 2 \pi t$$ , where $$y$$ in m 3. $$y(t)=4 \sin \left(\dfrac{\pi t}{2}\right)$$, where $$y$$ in m 4. $$y(t)=3 \cos \left(\dfrac{3 \pi \mathrm{t}}{2}\right)$$,  where $$y$$ in m

Subtopic:  Phasor Diagram |
75%
From NCERT
NEET - 2019
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A block of mass $$4~\text{kg}$$ hangs from a spring of spring constant $$k = 400~\text{N/m}$$. The block is pulled down through $$15~\text{cm}$$ below the equilibrium position and released. What is its kinetic energy when the block is $$10~\text{cm}$$ below the equilibrium position? [Ignore gravity]
1. $$5~\text{J}$$
2. $$2.5~\text{J}$$
3. $$1~\text{J}$$
4. $$1.9~\text{J}$$

Subtopic:  Energy of SHM |
77%
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Two springs, of force constants k1 and k2 are connected to a mass m as shown in the figure. The frequency of oscillation of the mass is f. If both k1 and k2 are made four times their original values, the frequency of oscillation will become:

 1 2f 2 f/2 3 f/4 4 4f
Subtopic:  Combination of Springs |
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A particle is executing SHM according to $$y = a \cos\omega t.$$ 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 |
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The potential energy of a particle oscillating along the $$x\text-$$axis is given as $$U = 20+(x-2)^2$$ where $$U$$ is in joules and $$x$$ in metres. The total mechanical energy of the particle is $$36~\text{J}$$. The maximum kinetic energy of the particle will be:
1. $$24~\text{J}$$
2. $$36~\text{J}$$
3. $$16~\text{J}$$
4. $$20~\text{J}$$
Subtopic:  Energy of SHM |
66%
From NCERT
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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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A particle executing simple harmonic motion has a kinetic energy of $$K_0 \cos^2(\omega t)$$. The values of the maximum potential energy and the total energy are, respectively:
1. $$0~\text{and}~2K_0$$
2. $$\frac{K_0}{2}~\text{and}~K_0$$
3. $$K_0~\text{and}~2K_0$$
4. $$K_0~\text{and}~K_0$$
Subtopic:  Energy of SHM |
62%
From NCERT
AIPMT - 2007
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A point performs simple harmonic oscillation of period $$\mathrm{T}$$ and the equation of motion is given by; $$x=a \sin (\omega t+\pi / 6)$$After the elapse of what fraction of the time period, the velocity of the point will be equal to half of its maximum velocity?
1. $$\frac{T}{8}$$

2. $$\frac{T}{6}$$

3. $$\frac{T}{3}$$

4. $$\frac{T}{12}$$

Subtopic:  Linear SHM |
70%
From NCERT
AIPMT - 2008
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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. $$2\pi \sqrt{\frac{q}{p}}$$
2. $$2\pi \sqrt{\frac{p}{q}}$$
3. $$2\pi \sqrt{\frac{q}{p+q}}$$
4. $$2\pi \sqrt{\frac{p}{p+q}}$$
Subtopic:  Energy of SHM |
73%
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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. $$\frac{T}{\sqrt{2}}$$
3. $$2T$$
4. $$\sqrt{2}T$$

Subtopic:  Spring mass system |
79%
From NCERT
AIPMT - 2010
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