Q. No.For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?
| 1. | \(x=0 \) | 2. | \(x= \pm A \) |
| 3. | \(x= \pm \dfrac{A}{\sqrt{2}}\) | 4. | \(x=\dfrac{A}{2}\) |
Subtopic: Energy of SHM |
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Level 1: 80%+
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A particle performing simple harmonic motion according to \(y = A \sin\omega t\). Then its kinetic energy \((K.E.),\) potential energy \((P.E.),\) and speed \((v)\) at the position \(Y=\dfrac{A}{2}\) are:
| 1. | \( { K.E. }=\dfrac{k A^2}{8} \\ { P.E. }=\dfrac{3 k A^2}{8} \\ v=\dfrac{A}{3} \sqrt{\dfrac{k}{m}} \) | 2. | \({ K.E. }=\dfrac{3 k A^2}{8} \\ { P.E. }=\dfrac{k A^2}{8} \\ v=\dfrac{A}{2} \sqrt{\dfrac{3 k}{m}} \) |
| 3. | \({ K.E. }=\dfrac{3 k A^2}{8} \\ { P.E. }=\dfrac{k A^2}{4} \\ v=A \sqrt{\dfrac{3 k}{m}} \) | 4. | \({ K.E. }=\dfrac{k A^2}{4} \\ { P.E. }=\dfrac{3 k A^2}{8} \\ v=\dfrac{A}{4} \sqrt{\dfrac{3 k}{m}} \) |
Subtopic: Energy of SHM |
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Level 1: 80%+
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The total energy of oscillation, of a particle executing SHM, is proportional to \(A^{\lambda};\) where \(A\) is the amplitude of oscillation and \(\lambda\) is a constant. Then, \(\lambda\) equals:
| 1. | \(2\) | 2. | \(4\) |
| 3. | \(-2\) | 4. | \(-4\) |
Subtopic: Energy of SHM |
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Level 1: 80%+
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A simple pendulum is oscillating with an angular frequency \(\omega\) and amplitude \(A.\) The displacement and velocity of the pendulum, when potential energy is half the total energy, are given by:
| 1. | \(\dfrac{A}{\sqrt{2}}, \dfrac{A}{\sqrt{2}} \omega\) | 2. | \(\dfrac{A}{2}, \dfrac{A}{2} \omega\) |
| 3. | \(\sqrt2A, 2A \omega\) | 4. | \(\sqrt2A, \sqrt2A \omega\) |
Subtopic: Energy of SHM |
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A body executes simple harmonic motion. The potential energy \((PE),\) kinetic energy \((KE)\) and total energy \((TE)\) are measured as a function of displacement \(x.\) Which of the following statements is true?
| 1. | \((TE)\) is zero when \(x = 0.\) |
| 2. | \((PE)\) is maximum when \(x = 0.\) |
| 3. | \((KE)\) is maximum when \(x = 0.\) |
| 4. | \((KE)\) is maximum when \(x\) is maximum. |
Subtopic: Energy of SHM |
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Level 1: 80%+
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A particle is performing simple harmonic motion (SHM), whose distance from the mean position varies as \(x = A~ \mathrm{sin} \omega t.\) What would be the position of the particle from the mean position where kinetic energy and potential energy are equal?
| 1. | \(\left({{{A}\over{2}}}\right)\) | 2. | \(\left({{{A}\over{\sqrt{2}}}}\right)\) |
| 3. | \(\left({{{A}\over{2\sqrt{2}}}}\right)\) | 4. | \(\left({{{A}\over{4}}}\right)\) |
Subtopic: Energy of SHM |
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A particle executes simple harmonic motion with a frequency of \(2\) Hz. The frequency with which its potential energy oscillates is:
1. \(4\) Hz
2. \(2\) Hz
3. \(6\) Hz
4. \(8\) Hz
Subtopic: Energy of SHM |
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For a particle performing simple harmonic motion, the maximum potential energy is \(25~\text{J}\). What is the kinetic energy of the particle when it is at half of its amplitude?
1. \(18.75~\text{kJ}\)
2. \(18.75~\text{J}\)
3. \(9.45~\text{kJ}\)
4. \(9.45~\text{J}\)
1. \(18.75~\text{kJ}\)
2. \(18.75~\text{J}\)
3. \(9.45~\text{kJ}\)
4. \(9.45~\text{J}\)
Subtopic: Energy of SHM |
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Level 1: 80%+
JEE
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A particle executes simple harmonic motion with amplitude, \(A.\) The displacement from the mean position at which its kinetic energy equals its potential energy is:
| 1. | \(\dfrac{A}2\) | 2. | \(\dfrac{A}{\sqrt{2}}\) |
| 3. | \(\dfrac{A \sqrt{2}}{3}\) | 4. | \(A \sqrt{2} \) |
Subtopic: Energy of SHM |
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A particle executing simple harmonic motion with amplitude \(A\) has the same potential and kinetic energies at the displacement:
| 1. | \(2\sqrt{A}\) | 2. | \(\dfrac{A}{2}\) |
| 3. | \(\dfrac{\mathrm{A}}{\sqrt{2}}\) | 4. | \(A\sqrt{2}\) |
Subtopic: Energy of SHM |
80%
Level 1: 80%+
NEET - 2024
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