Q. No.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. \(2\pi \sqrt{\frac{p}{p+q}}\)
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: Â Energy of SHM |
 73%
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Match List-I with List-II.
Choose the correct answer from the options given below:
| List-I (\(x \text{-}y\) graphs) |
List-II (Situations) |
||
| (a) |  |
(i) | Total mechanical energy is conserved |
| (b) |  |
(ii) | Bob of a pendulum is oscillating under negligible air friction |
| (c) |  |
(iii) | Restoring force of a spring |
| (d) |  |
(iv) | Bob of a pendulum is oscillating along with air friction |
Choose the correct answer from the options given below:
| (a) | (b) | (c) | (d) | |
| 1. | (iv) | (ii) | (iii) | (i) |
| 2. | (iv) | (iii) | (ii) | (i) |
| 3. | (i) | (iv) | (iii) | (ii) |
| 4. | (iii) | (ii) | (i) | (iv) |
Subtopic: Â Energy of SHM |
 85%
From NCERT
NEET - 2022
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A particle is executing simple harmonic motion with frequency \(f\). The frequency at which its kinetic energy changes into potential energy, will be:
1. \(\frac{f}{2}\)
2. \(f\)
3. \(2f\)
4. \(4f\)
1. \(\frac{f}{2}\)
2. \(f\)
3. \(2f\)
4. \(4f\)
Subtopic: Â Energy of SHM |
 63%
From NCERT
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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. \(K_0~\text{and}~K_0\)
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: Â Energy of SHM |
 63%
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AIPMT - 2007
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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: Â Energy of SHM |
 78%
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When the displacement is half the amplitude in an SHM, the ratio of potential energy to the total energy is:
1. \(\frac{1}{2}\)
2. \(\frac{1}{4}\)
3. \(1\)
4. \(\frac{1}{8}\)
1. \(\frac{1}{2}\)
2. \(\frac{1}{4}\)
3. \(1\)
4. \(\frac{1}{8}\)
Subtopic: Â Energy of SHM |
 82%
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A body is executing simple harmonic motion. At a displacement \(x,\) its potential energy is \(E_1\) and at a displacement \(y\), its potential energy is \(E_2\). The potential energy \(E\) at displacement \(x+y\) will be?
1. \(E = \sqrt{E_1}+\sqrt{E_2}\)
2. \(\sqrt{E} = \sqrt{E_1}+\sqrt{E_2}\)
3. \(E =E_1 +E_2\)
4. None of the above
Subtopic: Â Energy of SHM |
 56%
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If the potential energy \(U\) \((\text{in J})\) of a body executing SHM is given by \(U = 20+ 10(\sin^2 100\pi t),\) then the minimum potential energy of the body will be:
| 1. | Zero | 2. | \(30~\text{J}\) |
| 3. | \(20~\text{J}\) | 4. | \(40~\text{J}\) |
Subtopic: Â Energy of SHM |
 74%
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The kinetic energy \((K)\) of a simple harmonic oscillator varies with displacement \((x)\) as shown. The period of the oscillation will be: (mass of oscillator is \(1\) kg)
1. \(\frac{\pi}{2}~\text{s}\)
2. \(\frac{1}{2}~\text{s}\)
3. \(\pi~\text{s}\)
4. \(1~\text{s}\)
Subtopic: Â Energy of SHM |
 76%
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Equation of a simple harmonic motion is given by \(x= a\sin \omega t\). For which value of \(x\), kinetic energy is equal to the potential energy?
1. \(x = \pm a\)
2. \(x = \pm \frac{a}{2}\)
3. \(x = \pm \frac{a}{\sqrt{2}}\)
4. \(x = \pm \frac{\sqrt{3}a}{2}\)
1. \(x = \pm a\)
2. \(x = \pm \frac{a}{2}\)
3. \(x = \pm \frac{a}{\sqrt{2}}\)
4. \(x = \pm \frac{\sqrt{3}a}{2}\)
Subtopic: Â Energy of SHM |
 83%
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