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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 |

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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 $\frac{{T}^{\text{'}}}{T}$ will be:

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

3. | Zero | 4. | Infinite |

Subtopic: Energy of SHM |

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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-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 |

62%

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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 |

83%

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A particle executing SHM crosses points A and B with the same velocity. Having taken 3 s in passing from A to

B, it returns to B after another 3 s. The time period of the SHM will be:

1. | 15 s | 2. | 6 s |

3. | 12 s | 4. | 9 s |

Subtopic: Linear SHM |

54%

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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 of mass \(m\) and charge \(\text-q\) moves diametrically through a uniformly charged sphere of radius \(R\) with total charge \(Q\). The angular frequency of the particle's simple harmonic motion, if its amplitude \(<R\), is given by:

1. \(\sqrt{\dfrac{qQ}{4 \pi \varepsilon_0 ~mR} }\)

2. \(\sqrt{\dfrac{qQ}{4 \pi \varepsilon_0 ~mR^2} }\)

3. \(\sqrt{\dfrac{qQ}{4 \pi \varepsilon_0 ~mR^3}}\)

4. \( \sqrt{\dfrac{m}{4 \pi \varepsilon_0 ~qQ} }\)

Subtopic: Linear SHM |

57%

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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 \(\mathrm{x\text-}\)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 |

51%

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