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A particle moves in a circular path with a continuously increasing speed. Its motion is:

1. periodic

2. oscillatory

3. simple harmonic

4. none of them

Subtopic: Types of Motion |

52%

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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 |

81%

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NEET - 2022

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Trains travel between station A and station B: on the way up (from A to B) - they travel at a speed of \(80\) km/h, while on the return trip the trains travel at twice that speed. The services are maintained round the clock. Trains leave station A every \(30\) min for station B and reach B in \(2\) hrs. All trains operate continuously, without any rest at A or B.

1. | the frequency of trains leaving B must be twice as much as A. |

2. | the frequency of trains leaving B must be half as much as A. |

3. | the frequency of trains leaving B is equal to that at A |

4. | the situation is impossible to maintain unless larger number of trains are provided at A. |

Subtopic: Types of Motion |

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A particle undergoes SHM with an amplitude of \(10\) cm and a time period of \(4\) s. The average velocity of the particle during the course of its motion from its mean position to its extreme position is:

1. \(5\) cm/s

2. \(10\) cm/s

3. at least \(10\) cm/s

4. at most \(10\) cm/s

1. \(5\) cm/s

2. \(10\) cm/s

3. at least \(10\) cm/s

4. at most \(10\) cm/s

Subtopic: Simple Harmonic Motion |

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Two SHMs of the form:

\(x=A+A\text{sin}\omega t\\ y=A-A\text{sin}\omega t\)

are superposed on a particle, along \(x\) and \(y\) directions. The resultant of these motions is:

\(x=A+A\text{sin}\omega t\\ y=A-A\text{sin}\omega t\)

are superposed on a particle, along \(x\) and \(y\) directions. The resultant of these motions is:

1. | circular motion |

2. | \(x\)-axis | SHM along

3. | \(y\)-axis | SHM along

4. | \(x\) or \(y\)-axis | SHM, but along a direction other than

Subtopic: Simple Harmonic Motion |

52%

From NCERT

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A particle executes SHM along a straight line.

Statement I: |
A graph of its acceleration vs displacement (from mean position) is a straight line. |

Statement II: |
A graph of its velocity vs displacement (from mean position) is an ellipse. |

1. | Statement I is incorrect and Statement II is correct. |

2. | Both Statement I and Statement II are correct. |

3. | Both Statement I and Statement II are incorrect. |

4. | Statement I is correct and Statement II is incorrect. |

Subtopic: Simple Harmonic Motion |

70%

From NCERT

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The maximum speed and acceleration of a particle undergoing SHM are \(v_0\) and \(a_0,\) respectively. The time period of the SHM is:

1. \(\frac{2\pi v_0}{a_0}\)

2. \(\frac{2\pi a_0}{v_0}\)

3. \(\frac{v_0}{a_0}\)

4. \(\frac{2v_0}{a_0}\)

Subtopic: Simple Harmonic Motion |

79%

From NCERT

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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. | \(0.01\) Hz | 2. | \(0.02\) Hz |

3. | \(0.03\) Hz | 4. | \(0.04\) Hz |

Subtopic: Simple Harmonic Motion |

68%

From NCERT

AIPMT - 1998

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The time period of a particle in simple harmonic motion is equal to the time between consecutive appearances of the particle at a particular point in its motion. This point is:

1. | the mean position |

2. | an extreme position |

3. | between the mean position and the positive extreme |

4. | between the mean position and the negative extreme |

Subtopic: Simple Harmonic Motion |

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A particle moves in a plane such that its displacements are the sum of two displacements \(\overrightarrow {r_1}\) , and \(\overrightarrow {r_2};\) each of which undergo SHM in opposite phase with respect to the other, but of unequal amplitude. The resultant motion of the particle is:

1. | uniform circular motion |

2. | elliptical motion |

3. | linear SHM |

4. | angular SHM along a circle |

Subtopic: Simple Harmonic Motion |

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