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In a simple harmonic oscillation, the graph of acceleration against displacement for one complete oscillation will be:

1. an ellipse

2. a circle

3. a parabola

4. a straight line

Subtopic: Linear SHM |

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A particle executing SHM crosses points \(A\) and \(B\) with the same velocity. Having taken \(3~\text{s}\) in passing from \(A\) to

\(B\), it returns to \(B\) after another \(3~\text{s}\). The time period of the SHM will be:

\(B\), it returns to \(B\) after another \(3~\text{s}\). The time period of the SHM will be:

1. | \(15~\text{s}\) | 2. | \(6~\text{s}\) |

3. | \(12~\text{s}\) | 4. | \(9~\text{s}\) |

Subtopic: Linear SHM |

54%

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Which of the following examples represent simple harmonic motion?

1. | The rotation of the earth about its axis. |

2. | The motion of an oscillating mercury column in a \(U\text-\)tube. |

3. | General vibrations of a polyatomic molecule about its equilibrium position. |

4. | A fan rotating with a constant angular velocity. |

Subtopic: Simple Harmonic Motion |

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Which of the following relationships between the acceleration \(a\) and the displacement \(x\) of a particle involves simple harmonic motion?

1. \(a = 0 . 7 x\)

2. \(a = - 200 x^{2} \)

3. \(a = - 10 x\)

4. \(a = 100 x^{3}\)

Subtopic: Simple Harmonic Motion |

74%

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A spring having a spring constant of \(1200\) N/m is mounted on a horizontal table as shown in the figure. A mass of \(3\) kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of \(2.0\) cm and released. The frequency of oscillations will be:

1. | \(3.0~\text{s}^{-1}\) | 2. | \(2.7~\text{s}^{-1}\) |

3. | \(1.2~\text{s}^{-1}\) | 4. | \(3.2~\text{s}^{-1}\) |

Subtopic: Spring mass system |

72%

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Identify the correct definition:

1. | If after every certain interval of time, a particle repeats its motion, then the motion is called periodic motion. |

2. | To and fro motion of a particle is called oscillatory motion. |

3. | Oscillatory motion described in terms of single sine and cosine functions is called simple harmonic motion. |

4. | All of the above |

Subtopic: Types of Motion |

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A particle is executing SHM with time period \(T\). If the time period of its total mechanical energy is \(T'\), then \(\frac{T'}{T}\) will be:

1. | \(2\) | 2. | \(1 \over 2\) |

3. | Zero | 4. | Infinite |

Subtopic: Energy of SHM |

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The rotation of the earth about its axis is:

1. | periodic motion. |

2. | simple harmonic motion. |

3. | periodic and simple harmonic motion. |

4. | non-periodic motion. |

Subtopic: Types of Motion |

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All the surfaces are smooth and the system, given below, is oscillating with an amplitude \(\mathrm{A}.\) What is the extension of spring having spring constant \(\mathrm{k_1},\) when the block is at the extreme position?

1. | \({k_1 \over k_1+k_2} \text{A}\) | 2. | \({k_2A \over k_1+k_2}\) |

3. | \(\mathrm{A}\) | 4. | \(\text{A} \over 2\) |

Subtopic: Combination of Springs |

66%

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The displacement-time graph of a particle executing SHM is shown in the figure. Its displacement equation will be: (Time period = \(2\) second)

1. \(x= 10\sin\left(\pi t+\frac{\pi}{6}\right)\)

2. \(x= 10\sin\left(\pi t\right)\)

3. \(x= 10\cos\left(\pi t\right)\)

4. \(x= 5\sin\left(\pi t+\frac{\pi}{6}\right)\)

Subtopic: Linear SHM |

64%

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