Select the correct statements regarding potential energy \((U)\) in the simple harmonic motion of a particle along \(x\text-\)axis:

1. \(\frac{dU}{dx}<0\) for all positions of a particle performing SHM.
2. \(\frac{dU}{dx}>0\) for all time.
3. Potential energy is minimum at the equilibrium position of a particle performing SHM.
4. Potential energy increases linearly with the position as the particle moves away from the equilibrium position.

Subtopic:  Energy of SHM |
 72%
From NCERT
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A simple pendulum is pushed slightly from its equilibrium towards left and then set free to execute simple harmonic motion. Select the correct graph between its velocity(\(v\)) and displacement (\(x \)).

1. 2.
3.   4.
Subtopic:  Angular SHM |
 65%
From NCERT
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Simple harmonic motion is an example of:

1. uniformly accelerated motion
2. uniform motion
3. non-uniform accelerated motion
4. all of these

Subtopic:  Types of Motion |
 55%
From NCERT
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A particle under SHM takes 1.2 s to complete one vibration. Minimum time taken by it to travel from mean position to half of its amplitude is

1.  0.2 s

2.  0.1 s

3.  0.4 s

4.  0.3 s

Subtopic:  Simple Harmonic Motion |
 78%
From NCERT
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The potential energy of a particle executing SHM at the extreme position and mean position are 20 J and 5 J respectively. The kinetic energy of the particle at the mean position is:

1.  20 J

2.  5 J

3.  15 J

4.  12.5 J

Subtopic:  Energy of SHM |
 67%
From NCERT
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Equation of simple harmonic motion of a particle is y = (0.4 m) sin314t, where time t is in second. Frequency of vibration of the particle is

1.  100 Hz

2.  75 Hz

3.  50 Hz

4.  25 Hz

Subtopic:  Simple Harmonic Motion |
 87%
From NCERT
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A particle starts SHM from the mean position. Its amplitude is A and time period is T. At the time when its speed is half of its maximum speed, its displacement is

1.  A2

2.  A2

3.  A32

4.  2A3

Subtopic:  Simple Harmonic Motion |
 73%
From NCERT
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The acceleration of a particle in SHM is:

1. always zero.
2. always constant.
3. maximum at the extreme position.
4. maximum at the equilibrium position.

Subtopic:  Simple Harmonic Motion |
 84%
From NCERT
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A particle moves in the \(\mathrm{XY}-\) plane according to the equation \(\vec{r}=\left ( 5\hat{i}+3\hat{j} \right )\text{sin}(2t).\) The motion of the particle is along:

1. a straight line and is periodic.
2. a circle and is non-periodic.
3. an ellipse and is periodic.
4. a parabola and is non-periodic.
Subtopic:  Simple Harmonic Motion |
 52%
From NCERT
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A particle is performing SHM with amplitude \(A\) and angular velocity \(\omega.\) The ratio of the magnitude of maximum velocity to maximum acceleration is:
1. \(\omega\)
2. \(\frac{1}{\omega }\)

3. \(\omega^{2} \)
4. \(A\omega\)

Subtopic:  Simple Harmonic Motion |
 91%
From NCERT
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