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Kinetic energy of a particle executing simple harmonic motion in straight line is \(pv^2\) and potential energy is \(qx^2,\) where \(v\) is speed at distance \(x\) from the mean position. The time period of the SHM is given by the expression:

1. $2\mathrm{\pi}\sqrt{\frac{\mathrm{q}}{\mathrm{p}}}$

2. $2\mathrm{\pi}\sqrt{\frac{p}{q}}$

3. $2\mathrm{\pi}\sqrt{\frac{\mathrm{q}}{\mathrm{p}+\mathrm{q}}}$

4. $2\mathrm{\pi}\sqrt{\frac{p}{p+q}}$

Subtopic: Energy of SHM |

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The amplitude and the time period in an S.H.M. are 0.5 cm and 0.4 sec respectively. If the initial phase is $\mathrm{\pi}/2$ radian, then the equation of S.H.M. will be:

1. $\mathrm{y}=0.5\mathrm{sin}5\mathrm{\pi t}$

2. $\mathrm{y}=0.5\mathrm{sin}4\mathrm{\pi t}$

3. $\mathrm{y}=0.5\mathrm{sin}2.5\mathrm{\pi t}$

4. $\mathrm{y}=0.5\mathrm{cos}5\mathrm{\pi t}$

Subtopic: Linear SHM |

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In simple harmonic motion, the ratio of acceleration of the particle to its displacement at any time is a measure of:

1. | Spring constant | 2. | Angular frequency |

3. | (Angular frequency)^{2} |
4. | Restoring force |

Subtopic: Simple Harmonic Motion |

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One end of a spring of force constant \(\mathrm{k}\) is fixed to a vertical wall and the other to a block of mass \(\mathrm{m}\) resting on a smooth horizontal surface. There is another wall at a distance ${\mathrm{x}}_{0}$ from the block. The spring is then compressed by $2{\mathrm{x}}_{0}$ and then released. The time taken to strike the wall will be?

1. | \({1 \over 6} \pi \sqrt{ {k \over m}}\) | 2. | \( \sqrt{ {k \over m}}\) |

3. | \({2 \pi \over 3} \sqrt{ {m \over k}}\) | 4. | \({ \pi \over 4} \sqrt{ {k \over m}}\) |

Subtopic: Spring mass system |

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When the displacement is half the amplitude in an SHM, the ratio of potential energy to the total energy is:

1. 1 / 2

2. 1 / 4

3. 1

4. 1 / 8

Subtopic: Energy of SHM |

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A block is connected to a relaxed spring and kept on a smooth floor. The block is given a velocity towards the right. Just after this:

1. | the speed of block starts decreasing but acceleration starts increasing. |

2. | the speed of the block as well as its acceleration starts decreasing. |

3. | the speed of the block starts increasing but its acceleration starts decreasing. |

4. | the speed of the block as well as acceleration start increasing. |

Subtopic: Spring mass system |

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A simple pendulum of mass m swings about point B between extreme positions A and C. Net force acting on the bob at these three points is correctly shown by:

1. | 2. | ||

3. | 4. |

Subtopic: Angular SHM |

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The potential energy of a particle oscillating along the x-axis is given as U = 20+ (x–2)^{2} where U is in joules and x in meters. The total mechanical energy of the particle is 36 J. The maximum kinetic energy of the particle will be:

1. 24 J

2. 36 J

3. 16 J

4. 20 J

Subtopic: Energy of SHM |

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A particle is executing SHM according to y = a cos$\mathrm{\omega t}$. Then, which of the following graphs represent variations of potential energy?

1. I and III

2. II and IV

3. II and III

4. I and IV

Subtopic: Energy of SHM |

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Two springs, of force constants k_{1} and k_{2} are connected to a mass m as shown in the figure. The frequency of oscillation of the mass is f. If both k_{1} and k_{2} are made four times their original values, the frequency of oscillation will become:

1. | 2f | 2. | f/2 |

3. | f/4 | 4. | 4f |

Subtopic: Combination of Springs |

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