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Q. No.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. \(\frac{1}{8}\)
Subtopic: Energy of SHM |
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A block is connected to a relaxed spring and kept on a smooth floor. The block is given a velocity towards the right. Just after this:
| 1. | the speed of block starts decreasing but acceleration starts increasing. |
| 2. | the speed of the block as well as its acceleration starts decreasing. |
| 3. | the speed of the block starts increasing but its acceleration starts decreasing. |
| 4. | the speed of the block as well as acceleration start increasing. |
Subtopic: Spring mass system |
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A mass m is suspended from two springs of spring constant as shown in the figure below. The time period of vertical oscillations of the mass will be
1.
2.
3.
4.
Subtopic: Combination of Springs |
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One end of a spring of force constant \(k\) is fixed to a vertical wall and the other to a block of mass \(m\) resting on a smooth horizontal surface. There is another wall at a distance \(x_0\) from the block. The spring is then compressed by \(2x_0\)
| 1. | \(\frac{1}{6} \pi \sqrt{ \frac{k}{m}}\) | 2. | \( \sqrt{\frac{k}{m}}\) |
| 3. | \(\frac{2\pi}{3} \sqrt{ \frac{m}{k}}\) | 4. | \(\frac{\pi}{4} \sqrt{ \frac{k}{m}}\) |
Subtopic: Spring mass system |
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Which one of the following is not an example of simple harmonic motion?
| 1. | the motion of the Moon around the Earth as observed from Mars. |
| 2. | the ripples produced when a stone is dropped into a tank of water. |
| 3. | a weight moving up and down at the end of a spring. |
| 4. | the motion of a ball on the floor. |
Subtopic: Types of Motion |
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A mass is connected to a spring and it vibrates up and down, forming a simple harmonic system. Which of the following is/are correct?
| (a) | The kinetic energy of the mass is at a maximum halfway up. |
| (b) | The potential energy of the system is at a maximum at the top of the mass's motion. |
| (c) | The potential energy of the system is at a maximum at the bottom of the mass's motion. |
Choose the correct option from the given ones:
| 1. | (a), (b) and (c) | 2. | (a) and (b) only |
| 3. | (b) only | 4. | (c) only |
Subtopic: Simple Harmonic Motion |
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In simple harmonic motion, the ratio of acceleration of the particle to its displacement at any time is a measure of:
| 1. | Spring constant | 2. | Angular frequency |
| 3. | (Angular frequency)2 | 4. | Restoring force |
Subtopic: Simple Harmonic Motion |
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The amplitude and the time period in an SHM are \(0.5\) cm and \(0.4\) sec respectively. If the initial phase is \(\frac{\pi}{2}\) radian, then the equation of SHM will be:
1. \(y = 0.5\sin(5\pi t)\)
2. \(y = 0.5\sin(4\pi t)\)
3. \(y = 0.5\sin(2.5\pi t)\)
4. \(y = 0.5\cos(5\pi t)\)
1. \(y = 0.5\sin(5\pi t)\)
2. \(y = 0.5\sin(4\pi t)\)
3. \(y = 0.5\sin(2.5\pi t)\)
4. \(y = 0.5\cos(5\pi t)\)
Subtopic: Linear SHM |
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The angular velocities of three bodies in simple harmonic motion are \(\omega_1, \omega_2, \omega_3\) with their respective amplitudes as \(A_1, A_2, A_3.\) If all the three bodies have the same mass and maximum velocity, then:
| 1. | \(A_1 \omega_1=A_2 \omega_2=A_3 \omega_3\) |
| 2. | \(A_1 \omega_1^2=A_2 \omega_2^2=A_3 \omega_3^2\) |
| 3. | \(A_1^2 \omega_1=A_2^2 \omega_2=A_3^2 \omega_3\) |
| 4. | \(A_1^2 \omega_1^2=A_2^2 \omega_2^2=A^2\) |
Subtopic: Simple Harmonic Motion |
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The total energy of a particle, executing simple harmonic motion is:
1. \(\propto x\)
2. \(\propto x^2\)
3. Independent of \(x\)
4. \(\propto x^{\frac{1}{2}}\)
1. \(\propto x\)
2. \(\propto x^2\)
3. Independent of \(x\)
4. \(\propto x^{\frac{1}{2}}\)
Subtopic: Energy of SHM |
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