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The displacement of a particle is represented by the equation \(y= 3 \cos \left(\frac{\pi}{4}-\omega t \right)\). The motion of the particle is:

1. | simple harmonic with period \(\frac{2\pi}{\omega}\). |

2. | simple harmonic with period \(\frac{\pi}{\omega}\). |

3. | periodic but not simple harmonic. |

4. | non-periodic. |

Subtopic: Simple Harmonic Motion |

60%

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The displacement of a particle is represented by the equation y = ${\mathrm{sin}}^{3}$$\omega t$. The motion is

1. non-periodic

2. periodic but not simple harmonic

3. simple harmonic with period 2$\pi /\omega $

4. simple harmonic with period $\pi /\omega $

Subtopic: Simple Harmonic Motion |

70%

From NCERT

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The relations between acceleration and displacement of four particles are given below. Which one of the particles is executing simple harmonic motion?

1. \(a_1 = +2x\)

2. \(a_1= +2x^2\)

3. \(a_1= -2x^2\)

4. \(a_1 = -2x\)

Subtopic: Simple Harmonic Motion |

71%

From NCERT

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Motion of an oscillating liquid column in a U-tube is

1. | periodic but not simple harmonic |

2. | non-periodic |

3. | simple harmonic and time period is independent of the density of the liquid |

4. | simple harmonic and time period is directly proportional to the density of the liquid |

Subtopic: Simple Harmonic Motion |

56%

From NCERT

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A particle is acted simultaneously by mutually perpendicular simple harmonic motion x=acos$\omega t$ and y = asin$\omega t$. The trajectory of motion of the particle will be:

1. an ellipse

2. a parabola

3. a circle

4. a straight line

Subtopic: Simple Harmonic Motion |

64%

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The displacement of a particle varies with time according to the relation, \(y=asin \omega t+bcos \omega t.\)

1. | the motion is oscillatory but not SHM. |

2. | the motion is SHM with amplitude \(a+b.\) |

3. | the motion is SHM with amplitude \(a^{2}+b^{2}.\) |

4. | the motion is SHM with amplitude \(\sqrt{a^{2}+b^{2}}\). |

Subtopic: Simple Harmonic Motion |

89%

From NCERT

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Four pendulums A, B, C, and D are suspended from the same elastic support as shown in the figure. A and C are of the same length, while B is smaller than A and D is large than A. If A is given a transverse displacement,

1. D will vibrate with maximum amplitude

2. C will vibrate with maximum amplitude

3. B will vibrate with maximum amplitude

4. All four will oscillate with equal amplitude

Subtopic: Simple Harmonic Motion |

From NCERT

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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 x-projection of the radius vector of the rotating particle P will be:

1. $x\left(t\right)=B$ $\mathrm{sin}\left(\frac{2\mathrm{\pi t}}{30}\right)$

2. $x\left(t\right)=B$ $\mathrm{cos}\left(\frac{\mathrm{\pi t}}{15}\right)$

3. $x\left(t\right)=B$ $\mathrm{sin}\left(\frac{\mathrm{\pi t}}{15}+\frac{\mathrm{\pi}}{2}\right)$

4. $x\left(t\right)=B$ $\mathrm{cos}\left(\frac{\mathrm{\pi t}}{15}+\frac{\mathrm{\pi}}{2}\right)$

Subtopic: Simple Harmonic Motion | Phasor Diagram |

52%

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The equation of motion of a particle is x =$a\mathrm{cos}{(\alpha t)}^{2}$. The motion is:

1. periodic but not oscillatory

2. periodic and oscillatory

3. oscillatory but not periodic

4. neither periodic nor oscillatory

Subtopic: Simple Harmonic Motion |

From NCERT

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A particle executing SHM has a maximum speed of \(30\) cm/s and a maximum acceleration of \(60\) cm/s^{2}. The period of oscillation is:

1. \(\pi \) s

2. \(\frac{\pi }{2}\) s

3. \(2\pi\) s

4. \(\frac{\pi }{4}\) s

Subtopic: Simple Harmonic Motion |

85%

From NCERT

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