A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s2 at a distance of 5 m from the mean position. The time period of oscillation is:

1. 2π s 2. π s
3. 2 s 4. 1 s

Subtopic:  Angular SHM |
 84%
From NCERT
NEET - 2018
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A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. 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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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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