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Q. No.Given below are two statements:
Assertion (A):
The combination of \(y=\text{sin}\omega t+\text{cos}2\omega t\) is not a simple harmonic function even though it is periodic.
Reason (R):
All periodic functions satisfy the relation \( \dfrac{d^{2} y}{d t^{2}}=-k y \).
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.
Both (A) and (R) are False.
Subtopic: Simple Harmonic Motion |
Level 3: 35%-60%
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A particle executes simple harmonic motion between \(x=-A\) and \(x=+A.\) The time taken for it to move from \(0\) to \(A/2\) is \(T_1\) and the time to move from \(A/2\) to \(A\) is \(T_2.\) Then:
1. \(T_{1}<T_{2}\)
2. \(T_{1}>T_{2}\)
3. \(T_{1}=T_{2}\)
4. \(T_{1}=2 T_{2}\)
1. \(T_{1}<T_{2}\)
2. \(T_{1}>T_{2}\)
3. \(T_{1}=T_{2}\)
4. \(T_{1}=2 T_{2}\)
Subtopic: Linear SHM |
74%
Level 2: 60%+
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A body is performing simple harmonic motion with an amplitude of \(10~\text{cm}.\) The velocity of the body was tripled by air jet when it is at \(5~\text{cm}\) from its mean position. The new amplitude of vibration is \(\sqrt x~\text{cm}.\) The value of \(x \) is:
| 1. | \(500\) | 2. | \(600\) |
| 3. | \(700\) | 4. | \(800\) |
Subtopic: Simple Harmonic Motion |
66%
Level 2: 60%+
JEE
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A block of mass \(M\) is connected to a spring constant \(k.\) It oscillates on the frictionless inclined surface as shown in the figure. The time period of oscillation is:
| 1. | \(T=2 \pi \sqrt{\dfrac{M}{k}}\) | 2. | \(T=2 \pi \sqrt{\dfrac{k}{M}}\) |
| 3. | \(T=\dfrac{1}{2 \pi} \sqrt{\dfrac{k}{M}}\) | 4. | \(T=2 \pi \sqrt{\dfrac{M}{k}} \sin \theta\) |
Subtopic: Spring mass system |
81%
Level 1: 80%+
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A body executing SHM has a maximum speed of \(30~\text{cm s}^{-1}\) and a maximum acceleration of \(60~\text{cm s}^{-2}.\) What is the time period of the oscillating body in seconds?
| 1. | \(\pi\) | 2. | \(\pi/2\) |
| 3. | \(2\pi\) | 4. | \(\pi/4\) |
Subtopic: Simple Harmonic Motion |
90%
Level 1: 80%+
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On average, a human heart is found to beat \(72\) times per minute. The frequency of heartbeat will be:
1. \(0.833~\text s^{-1}\)
2. \(1.2~\text s^{-1}\)
3. \(12~\text s^{-1}\)
4. \(72~\text s^{-1}\)
1. \(0.833~\text s^{-1}\)
2. \(1.2~\text s^{-1}\)
3. \(12~\text s^{-1}\)
4. \(72~\text s^{-1}\)
Subtopic: Types of Motion |
72%
Level 2: 60%+
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A body oscillates with simple harmonic motion according to the equation (in SI units),
\(x=5 \cos \left(2 \pi t+\dfrac{\pi}{3}\right) \)
The displacement of the body at a time \(t=1.5~\text s\) is:
1. \(-5~\text m\)
2. \(-2.5~\text m\)
3. \(-2.0~\text m\)
4. \(-1.0~\text m\)
\(x=5 \cos \left(2 \pi t+\dfrac{\pi}{3}\right) \)
The displacement of the body at a time \(t=1.5~\text s\) is:
1. \(-5~\text m\)
2. \(-2.5~\text m\)
3. \(-2.0~\text m\)
4. \(-1.0~\text m\)
Subtopic: Simple Harmonic Motion |
79%
Level 2: 60%+
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The time period of a simple pendulum in a stationary lift is \(T.\) If the lift accelerates upward with an acceleration of \(\dfrac g 6\) (where \(g\) is the acceleration due to gravity), then the time period of the pendulum would be:
| 1. | \(\sqrt{\dfrac{6}{5}} ~T \) | 2. | \(\sqrt{\dfrac{5}{6}} ~T\) |
| 3. | \(\sqrt{\dfrac{6}{7}}~T\) | 4. | \(\sqrt{\dfrac{7}{6}} ~T\) |
Subtopic: Angular SHM |
80%
Level 1: 80%+
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\((\text{sin}\omega t+\text{cos}\omega t)\) is a periodic function, its time period will be:
| 1. | \(\dfrac{\pi}{\omega}\) | 2. | \(\dfrac{2\pi}{\omega}\) |
| 3. | \(\dfrac{1}{\omega}\) | 4. | \(\dfrac{\omega}{2\pi}\) |
Subtopic: Types of Motion |
86%
Level 1: 80%+
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Identify the function which represents a non-periodic motion?
| 1. | \(e^{-\omega t} \) | 2. | \(\text{sin}\omega t\) |
| 3. | \(\text{sin}\omega t+\text{cos}\omega t\) | 4. | \(\text{sin}(\omega t+\pi/4) \) |
Subtopic: Types of Motion |
83%
Level 1: 80%+
NEET - 2022
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