Q. No.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%
From NCERT
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The oscillation of a body on a smooth horizontal surface is represented by the equation, \(X=A \text{cos}(\omega t)\),
where \(X=\) displacement at time \(t,\) \(\omega=\) frequency of oscillation.
Which one of the following graphs correctly shows the variation of acceleration, \(a\) with time, \(t?\)
(\(T=\) time period)
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Simple Harmonic Motion |
67%
From NCERT
AIPMT - 2014
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The distance covered by a particle undergoing SHM in one time period is: (amplitude = A)
1. zero
2. A
3. 2 A
4. 4 A
Subtopic: Simple Harmonic Motion |
76%
From NCERT
NEET - 2019
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An SHM has an amplitude \(a\) and a time period \(T.\) The maximum velocity will be:
1. \({4a \over T}\)
2. \({2a \over T}\)
3. \({2 \pi \over T}\)
4. \({2a \pi \over T}\)
1. \({4a \over T}\)
2. \({2a \over T}\)
3. \({2 \pi \over T}\)
4. \({2a \pi \over T}\)
Subtopic: Simple Harmonic Motion |
91%
From NCERT
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The displacement of a particle executing simple harmonic motion is given by, \(y = A_{0} + A\sin \omega t+ B \cos\omega t.\)
Then the amplitude of its oscillation is given by:
Then the amplitude of its oscillation is given by:
| 1. | \(A + B\) | 2. | \(A_{0}\) \(+\) \(\sqrt{A^{2} + B^{2}}\) |
| 3. | \(\sqrt{A^{2} + B^{2}}\) | 4. | \(\sqrt{A_{0}^{2}+\left( A + B \right)^{2}}\) |
Subtopic: Simple Harmonic Motion |
59%
From NCERT
NEET - 2019
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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. \(5~\text {cm}, 2~\text s\)
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 |
75%
From NCERT
NEET - 2024
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A particle is executing a simple harmonic motion. Its maximum acceleration is and maximum velocity is . Then its time period of vibration will be:
| 1. | \(\frac {\beta^2}{\alpha^2}\) | 2. | \(\frac {\beta}{\alpha}\) |
| 3. | \(\frac {\beta^2}{\alpha}\) | 4. | \(\frac {2\pi \beta}{\alpha}\) |
Subtopic: Simple Harmonic Motion |
85%
From NCERT
NEET - 2015
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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 |
91%
From NCERT
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The average velocity of a particle executing SHM in one complete vibration is:
1. zero
2. \(\dfrac{A \omega}{2}\)
3. \(A \omega\)
4. \(\dfrac{A \left(\omega\right)^{2}}{2}\)
Subtopic: Simple Harmonic Motion |
73%
From NCERT
NEET - 2019
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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%
From NCERT
AIPMT - 1998
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