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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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Level 1: 80%+
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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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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. \(9.45~\text{J}\)
Subtopic:  Energy of SHM |
 84%
Level 1: 80%+
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Which, of the following, is true for a simple pendulum undergoing small oscillations?
(neglect all dissipative forces)
1. Kinetic energy is conserved
2. Momentum is conserved
3. Potential energy is conserved
4. Total energy is conserved
Subtopic:  Energy of SHM |
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Level 2: 60%+

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If a simple pendulum oscillates with small amplitude \(\left(A_0\right)\) then the total energy of oscillations can be given by: 
(symbols have usual meanings)
1. \(\dfrac{m g A_0^2}{2l}\)
2. \(\dfrac{m g l}{4 \pi A_0}\)
3. \(\dfrac{m g A_0^2}{3 l}\)
4. \(\dfrac{m g A_0^2}{4 \pi^2}\)
Subtopic:  Energy of SHM |
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Level 2: 60%+
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A particle executes simple harmonic motion (SHM) along the \(x\text-\)axis with amplitude \(A\) about the origin. What is the ratio of the particle's kinetic energy to its total energy when its displacement is \(x=\dfrac{A}{3} \text{?}\)
1. \(\dfrac{8}{9}\) 2. \(\dfrac{7}{8}\)
3. \(\dfrac{1}{9}\) 4. \(\dfrac{1}{8}\)
Subtopic:  Energy of SHM |
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Level 2: 60%+
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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)

1. 2.
3.   4.
Subtopic:  Energy of SHM |
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