Q. No.For a simple pendulum, a graph is plotted between its kinetic energy (\(KE\)) and potential energy (\(PE\)) against its displacement \(d\). Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)
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Subtopic: Energy of SHM |
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A particle executes simple harmonic motion with a time period \(T.\) It starts at its equilibrium position at \(t=0.\) How will the graph of its kinetic energy \((KE)\) versus time \((t)\) look like?
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Subtopic: Energy of SHM |
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Level 2: 60%+
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A body of mass \(M\) and a charge \(q\) is connected to a spring of spring constant \(k.\) It oscillates along the \(x\text{-direction}\) about its equilibrium position, taken to be at \(x = 0,\) with an amplitude \(A.\) An electric field \(E\) is applied along the \(x\text{-direction}. \)
Which of the following statements is correct?
Which of the following statements is correct?
| 1. | The total energy of the system is \(\dfrac{1}{2}m\omega^2A^2+\dfrac{1}{2}\dfrac{q^2E^2}{k}.\) |
| 2. | The new equilibrium position is at a distance \(\dfrac{2qE} {k}\) from \(x = 0.\) |
| 3. | The new equilibrium position is at a distance \(\dfrac{qE} {2k}\) from \(x = 0.\) |
| 4. | The total energy of the system is \(\dfrac{1}{2}m\omega^2A^2-\dfrac{1}{2}\dfrac{q^2E^2}{k}.\) |
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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For a particle undergoing linear simple harmonic motion (SHM), the graph showing the variation of kinetic energy, \(K\) with position, \(x\) of the particle is:
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Subtopic: Energy of SHM |
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A body is doing SHM with amplitude \(A.\) When it is at \(x = +\dfrac{A}{2},\) the ratio of kinetic energy to potential energy would be:
1. \(1:1\)
2. \(3:1\)
3. \(2:1\)
4. \(4:1\)
1. \(1:1\)
2. \(3:1\)
3. \(2:1\)
4. \(4:1\)
Subtopic: Energy of SHM |
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Which graph correctly represents the difference \((d)\) between the total energy and the potential energy of a particle in linear simple harmonic motion (SHM) as a function of its position \(x,\) where \(x=0\) denotes the mean position?
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Subtopic: Energy of SHM |
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A particle is performing SHM having position \( x = A~\text {cos} (30^\circ) , \) and \(A = 40 ~\text {cm} \). If its kinetic energy at this position is \(200\) J, then the value of force constant is:
1. \(10~\text{kN/m}\)
2. \(20~\text{kN/m}\)
3. \(10000~\text{kN/m}\)
4. \(20000~\text{kN/m}\)
1. \(10~\text{kN/m}\)
2. \(20~\text{kN/m}\)
3. \(10000~\text{kN/m}\)
4. \(20000~\text{kN/m}\)
Subtopic: Energy of SHM |
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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 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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