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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A mass of \(2.0\) kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes a simple harmonic motion. The spring constant is \(200\) N/m. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan? 
(Take \(g=10\) m/s2
                

1. \(8.0\) cm
2. \(10.0\) cm
3. any value less than \(12.0\) cm
4. \(4.0\) cm
Subtopic:  Combination of Springs |
 78%
From NCERT
AIPMT - 2007
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The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is:
1. 0.5π
2. π
3. 0.707π
4. zero

Subtopic:  Simple Harmonic Motion |
 74%
From NCERT
AIPMT - 2007
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A rectangular block of mass m and area of cross-section A floats in a liquid of density ρ. If it is given a small vertical displacement from equilibrium, it undergoes oscillation with a time period T. Then:
1. Tρ
2. T1A
3. T1ρ
4. T1m

Subtopic:  Simple Harmonic Motion |
 51%
From NCERT
AIPMT - 2006
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The displacement of a particle executing simple harmonic motion is given by,

y=A0+A sinωt + B cosωt.
Then the amplitude of its oscillation is given by:
1. A+B
2. A0 + A2+B2
3. A2+B2
4. A02 + (A+B)2

Subtopic:  Simple Harmonic Motion |
 56%
From NCERT
NEET - 2019
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The average velocity of a particle executing SHM in one complete vibration is:
1. zero
2. Aω2
3. Aω
4. Aω22

Subtopic:  Simple Harmonic Motion |
 70%
From NCERT
NEET - 2019
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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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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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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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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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