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. \(2 \pi \sqrt{\frac{x_{1}^{2}+x_{2}^{2}}{v_{1}^{2}+v_{2}^{2}}}~\) 2. \(2 \pi \sqrt{\frac{{x}_{2}^{2}-{x}_{1}^{2}}{{v}_{1}^{2}-{v}_{2}^{2}}}\)
3. \(2 \pi \sqrt{\frac{v_{1}^{2}+v_{2}^{2}}{x_{1}^{2}+x_{2}^{2}}}\) 4. \(2 \pi \sqrt{\frac{v_{1}^{2}-v_{2}^{2}}{x_{1}^{2}-x_{2}^{2}}}\)

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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Out of the following functions, which represents SHM?
I. y=sin ωt-cos ωt
II. y=sin3 ωt
III. y=5 cos3π4-3ωt
IV. y=1+ωt+ω2t2

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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A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a and time period T. The speed of the pendulum at x=a2 will be:
1. \(\frac{\pi a\sqrt3}{2T}\)
2. \(\frac{\pi a}{T}\)
3. \(\frac{3\pi^2 a}{T}\)
4. \(\frac{\pi a\sqrt3}{T}\)
Subtopic:  Simple Harmonic Motion |
 81%
From NCERT
AIPMT - 2009
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Which one of the following equations of motion represents simple harmonic motion where k, k0, k1, and a are all positive? 
1. Acceleration = -k0x + k1x2
2. Acceleration = -k(x+a)
3. Acceleration = k(x+a)
4. Acceleration = kx
Subtopic:  Simple Harmonic Motion |
 78%
From NCERT
AIPMT - 2009
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Two simple harmonic motions of angular frequencies 100 and 1000 rad s-1 have the same displacement amplitude. The ratio of their maximum acceleration is:

1. 1: 10
2. 1: 102
3. 1: 103
4. 1: 104

Subtopic:  Simple Harmonic Motion |
 88%
From NCERT
AIPMT - 2008
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Two points are located at a distance of \(10\) m and \(15\) m from the source of oscillation. The period of oscillation is \(0.05\) s and the velocity of the wave is \(300\) m/s. What is the phase difference between the oscillations of two points?
1. \(\frac{\pi}{3}\)
2. \(\frac{2\pi}{3}\)
3. \(\pi\)
4. \(\frac{\pi}{6}\)

Subtopic:  Simple Harmonic Motion |
 76%
From NCERT
AIPMT - 2008
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A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is:
1. T4
2. T8
3. T12
4. T2

Subtopic:  Simple Harmonic Motion |
 82%
From NCERT
AIPMT - 2007
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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. \(0\) and \(2K_0\)
2. \(\frac{K_0}{2}\) and \(K_0\)
3. \(K_0\) and \(2K_0\)
4. \(K_0\) and \(K_0\)

Subtopic:  Energy of SHM |
 62%
From NCERT
AIPMT - 2007
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