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Two identical masses are connected by a spring of spring constant \(k,\) and the individual masses are observed to undergo SHM with their centre of mass remaining at rest. The amplitude of oscillation of one of the masses is \(A.\) The total energy of oscillation is:
| 1. | \({\Large\frac{1}{2}}kA^2\) | 2. | \(kA^2\) |
| 3. | \(2kA^2\) | 4. | \(4kA^2\) |
Subtopic: Energy of SHM |
Level 4: Below 35%
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Given below are two statements:
| Statement I: | If the acceleration of a particle is directed towards a fixed point, and proportional to the distance from that point – the motion is SHM. |
| Statement II: | During SHM, the kinetic energy of the particle oscillates at twice the frequency of the SHM. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Energy of SHM |
Level 3: 35%-60%
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A particle of mass \(m\) executes SHM along a straight line with an amplitude \(A\) and frequency \(f.\)
| Assertion (A): | The kinetic energy of the particle undergoes oscillation with a frequency \(2f.\) |
| Reason (R): | Velocity of the particle, \(v = {\dfrac{dx}{dt}}\), its kinetic energy equals \({\dfrac 12}mv^2\) and the particle oscillates sinusoidally with a frequency \(f\). |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Energy of SHM |
52%
Level 3: 35%-60%
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