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Which of the following examples represent periodic motion?

1. | A swimmer completing one (return) trip from one bank of a river to the other and back. |

2. | A freely suspended bar magnet displaced from its N-S direction and released. |

3. | Swaying of the branches of the tree. |

4. | An arrow released from a bow. |

Subtopic: Types of Motion |

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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 |

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Subtopic: Types of Motion |

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The period of \((\sin\omega t-\cos\omega t)\) is:

1. \(\frac{\pi}{\omega}\)

2. \(\frac{4 \pi}{\omega}\)

3. \(\frac{3 \pi}{\omega}\)

4. \(\frac{2 \pi}{\omega}\)

1. \(\frac{\pi}{\omega}\)

2. \(\frac{4 \pi}{\omega}\)

3. \(\frac{3 \pi}{\omega}\)

4. \(\frac{2 \pi}{\omega}\)

Subtopic: Simple Harmonic Motion |

74%

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$y={\mathrm{sin}}^{3}\omega tis$:

1. | a simple harmonic function. |

2. | a simple harmonic function but not a periodic function. |

3. | both periodic and simple harmonic function. |

4. | only periodic function. |

Subtopic: Simple Harmonic Motion |

66%

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A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. (Take the direction from A to B as the positive direction.) The signs of velocity, acceleration, and force on the particle when it is at 3 cm away from A going towards B are:

1. Zero, Negative, Negative

2. Negative, Zero, Zero

3. Negative, Negative, Negative

4. Positive, Positive, Positive

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 |

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A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?

1. 219 N

2. 196 N

3. 223 N

4. 225 N

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 |

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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 maximum acceleration of the mass is:

1. | \(6\) ms^{–2} |
2. | \(8\) ms^{–}^{2} |

3. | \(3.3\) ms^{–}^{2} |
4. | \(5.1\) ms^{–}^{2} |

Subtopic: Combination of Springs |

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