Q. No.The velocity-time diagram of a harmonic oscillator is shown in the figure given below. The frequency of oscillation will be:
1. \(25~\text{Hz}\)
2. \(50~\text{Hz}\)
3. \(12.25~\text{Hz}\)
4. \(33.3~\text{Hz}\)
Subtopic: Simple Harmonic Motion |
75%
Level 2: 60%+
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The motion of a particle varies with time according to the relation \(y= a\sin\omega t+ a\cos \omega t\). Then:
| 1. | the motion is oscillatory but not SHM. |
| 2. | the motion is SHM with an amplitude \(a\sqrt{2}\). |
| 3. | the motion is SHM with an amplitude \(\sqrt{2}\). |
| 4. | the motion is SHM with an amplitude \(a\). |
Subtopic: Simple Harmonic Motion |
73%
Level 2: 60%+
Hints
The equation of motion of a particle is \({d^2y \over dt^2}+Ky=0 \) where \(K\) is a positive constant. The time period of the motion is given by:
| 1. | \(2 \pi \over K\) | 2. | \(2 \pi K\) |
| 3. | \(2 \pi \over \sqrt{K}\) | 4. | \(2 \pi \sqrt{K}\) |
Subtopic: Simple Harmonic Motion |
77%
Level 2: 60%+
Hints
The displacement versus time curve for a particle executing SHM is shown in the figure.
Choose the correct statement/s.
| 1. | The phase of the oscillator is the same at \(t = 0~\text{s}~\text{and}~t = 2~\text{s}\). |
| 2. | The phase of the oscillator is the same at \(t = 2~\text{s}~\text{and}~t = 6~\text{s}\). |
| 3. | The phase of the oscillator is the same at \(t = 1~\text{s}~\text{and}~t = 7~\text{s}\). |
| 4. | The phase of the oscillator is the same at \(t = 1~\text{s}~\text{and}~t = 5~\text{s}\). |
Choose the correct statement/s.
| 1. | \(1,2~\text{and}~4\) | 2. | \(1~\text{and}~3\) |
| 3. | \(2~\text{and}~4\) | 4. | \(3~\text{and}~4\) |
Subtopic: Simple Harmonic Motion |
72%
Level 2: 60%+
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The displacement of a particle along the \(x\text-\)axis is given by \(x= a\sin^2\omega t\). The motion of the particle corresponds to:
| 1. | simple harmonic motion of frequency \(\frac{\omega}{\pi}\). |
| 2. | simple harmonic motion of frequency \(\frac{3\omega}{2\pi}\). |
| 3. | non-simple harmonic motion. |
| 4. | simple harmonic motion of frequency \(\frac{\omega}{2\pi}\). |
Subtopic: Simple Harmonic Motion |
Level 4: Below 35%
NEET - 2010
Hints
If the time of mean position from amplitude (extreme) position is \(6\) seconds, then the frequency of SHM will be:
| 1. | \(0.01~\text{Hz}\) | 2. | \(0.02~\text{Hz}\) |
| 3. | \(0.03~\text{Hz}\) | 4. | \(0.04~\text{Hz}\) |
Subtopic: Simple Harmonic Motion |
70%
Level 2: 60%+
AIPMT - 1998
Hints
If \(x = 5 \mathrm {sin }\left(\pi t+ {\dfrac {\pi} 3}\right)~\text m\) represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively are:
| 1. | \(5~\text m, 2~\text s\) | 2. | \(5~\text {cm}, 1~\text s\) |
| 3. | \(5~\text m, 1~\text s\) | 4. | \(5~\text {cm}, 2~\text s\) |
Subtopic: Simple Harmonic Motion |
73%
Level 2: 60%+
NEET - 2024
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The figure shows the circular motion of a particle. The radius of the circle, the period, the sense of revolution, and the initial position are indicated in the figure. The simple harmonic motion of the \({x\text-}\)projection of the radius vector of the rotating particle \(P\) will be:
1. \(x \left( t \right) = B\text{sin} \left(\dfrac{2 πt}{30}\right)\)
2. \(x \left( t \right) = B\text{cos} \left(\dfrac{πt}{15}\right)\)
3. \(x \left( t \right) = B\text{sin} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)\) \(\)
4. \(x \left( t \right) = B\text{cos} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)\)
Subtopic: Simple Harmonic Motion | Phasor Diagram |
53%
Level 3: 35%-60%
Hints
The variation of acceleration, \(a\) of a particle executing SHM with displacement \(x\) is:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Simple Harmonic Motion |
70%
Level 2: 60%+
Hints
Which one of the following equations of motion represents simple harmonic motion? (where \(k,k_0,k_1~\text{and}~a\) are all positive.)
1. Acceleration \(=-k_0x+k_1x^2\)
2. Acceleration \(=-k(x+a)\)
3. Acceleration \(=k(x+a)\)
4. Acceleration \(=kx\)
1. Acceleration \(=-k_0x+k_1x^2\)
2. Acceleration \(=-k(x+a)\)
3. Acceleration \(=k(x+a)\)
4. Acceleration \(=kx\)
Subtopic: Simple Harmonic Motion |
75%
Level 2: 60%+
NEET - 2009
Hints
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