A particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta$. Then its time period of vibration will be:

 1 $$\frac {\beta^2}{\alpha^2}$$ 2 $$\frac {\beta}{\alpha}$$ 3 $$\frac {\beta^2}{\alpha}$$ 4 $$\frac {2\pi \beta}{\alpha}$$

Subtopic:  Simple Harmonic Motion |
84%
From NCERT
NEET - 2015
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When two displacements are represented by $$y_1 = a \text{sin}(\omega t)$$ and $$y_2 = b\text{cos}(\omega t)$$ are superimposed, then the motion is:

 1 not simple harmonic. 2 simple harmonic with amplitude $$\frac{a}{b}$$. 3 simple harmonic with amplitude $$\sqrt{a^2+b^{2}}.$$ 4 simple harmonic with amplitude $$\frac{a+b}{2}$$.
Subtopic:  Simple Harmonic Motion |
91%
From NCERT
NEET - 2015
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A particle is executing SHM along a straight line. Its velocities at distances $$x_1$$ and $$x_2$$ from the mean position are $$v_1$$ and $$v_2$$, respectively. Its time period is:

 1 $$2 \pi \sqrt{\dfrac{x_{1}^{2}+x_{2}^{2}}{v_{1}^{2}+v_{2}^{2}}}~$$ 2 $$2 \pi \sqrt{\dfrac{{x}_{2}^{2}-{x}_{1}^{2}}{{v}_{1}^{2}-{v}_{2}^{2}}}$$ 3 $$2 \pi \sqrt{\dfrac{v_{1}^{2}+v_{2}^{2}}{x_{1}^{2}+x_{2}^{2}}}$$ 4 $$2 \pi \sqrt{\dfrac{v_{1}^{2}-v_{2}^{2}}{x_{1}^{2}-x_{2}^{2}}}$$
Subtopic:  Simple Harmonic Motion |
73%
From NCERT
NEET - 2015
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The oscillation of a body on a smooth horizontal surface is represented by the equation, $$X=A \text{cos}(\omega t)$$,
where $$X=$$ displacement at time $$t,$$ $$\omega=$$ frequency of oscillation.
Which one of the following graphs correctly shows the variation of acceleration, $$a$$ with time, $$t?$$
($$T=$$ time period) $$a~~O~~T~~t~~$$

 1 2 3 4

Subtopic:  Simple Harmonic Motion |
65%
From NCERT
AIPMT - 2014
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A particle of mass $$m$$ oscillates along $${x}\text-$$axis according to equation $$x = a\text{sin}\omega t.$$ The nature of the graph between momentum and displacement of the particle is:
 1 circle 2 hyperbola 3 ellipse 4 straight line passing through the origin
Subtopic:  Types of Motion |
57%
From NCERT
NEET - 2013
Hints

Out of the following functions, which represents SHM?
$\mathrm{I}.$ $\mathrm{y}=\mathrm{sin}$ $\mathrm{\omega t}-\mathrm{cos}$ $\mathrm{\omega t}$
$\mathrm{II}.$ $\mathrm{y}={\mathrm{sin}}^{3}$ $\mathrm{\omega t}$
$\mathrm{III}.$ $\mathrm{y}=5$ $\mathrm{cos}\left(\frac{3\mathrm{\pi }}{4}-3\mathrm{\omega t}\right)$
$\mathrm{IV}.$ $\mathrm{y}=1+\mathrm{\omega t}+{\mathrm{\omega }}^{2}{\mathrm{t}}^{2}$

1.  Only (IV) does not represent SHM
2.  (I) and (III)
3.  (I) and (II)
4.  Only (I)

Subtopic:  Simple Harmonic Motion |
70%
From NCERT
AIPMT - 2011
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A particle of mass $$m$$ is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time?

 1 2 3 4
Subtopic:  Energy of SHM |
From NCERT
AIPMT - 2011
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Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie in a straight line perpendicular to the paths of the two particles. The phase difference is:

 1 π / 6 2 0 3 2 π / 3 4 π
Subtopic:  Linear SHM |
56%
From NCERT
AIPMT - 2011
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The displacement of a particle along the x-axis is given by, x = asin2$\mathrm{\omega }$t. The motion of the particle corresponds to:

 1 simple harmonic motion of frequency $\frac{\mathrm{\omega }}{\mathrm{\pi }}$ 2 simple harmonic motion of frequency $\frac{3\mathrm{\omega }}{2\mathrm{\pi }}$ 3 non-simple harmonic motion 4 simple harmonic motion of frequency $\frac{\mathrm{\omega }}{2\mathrm{\pi }}$

$\frac{\mathrm{}}{}$

Subtopic:  Simple Harmonic Motion |
From NCERT
AIPMT - 2010
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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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