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The radius of the circle, the period of revolution, initial position and direction of revolution are indicated in the figure.

The \(y\)-projection of the radius vector of rotating particle \(P\) will be:

1. \(y(t)=3 \cos \left(\dfrac{\pi \mathrm{t}}{2}\right)\), where \(y\) in m

2. \(y(t)=-3 \cos 2 \pi t\) , where \(y\) in m

3. \(y(t)=4 \sin \left(\dfrac{\pi t}{2}\right)\), where \(y\) in m

4. \(y(t)=3 \cos \left(\dfrac{3 \pi \mathrm{t}}{2}\right) \), where \(y\) in m

Subtopic: Phasor Diagram |

75%

From NCERT

NEET - 2019

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A block of mass \(4~\text{kg}\) hangs from a spring of spring constant \(k = 400~\text{N/m}\). The block is pulled down through \(15~\text{cm}\) below the equilibrium position and released. What is its kinetic energy when the block is \(10~\text{cm}\) below the equilibrium position? **[**Ignore gravity**]**

1. \(5~\text{J}\)

2. \(2.5~\text{J}\)

3. \(1~\text{J}\)

4. \(1.9~\text{J}\)

Subtopic: Energy of SHM |

77%

From NCERT

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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 |

73%

From NCERT

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A particle is executing SHM according to \(y = a \cos\omega t.\) 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 |

60%

From NCERT

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

1. \(24~\text{J}\)

2. \(36~\text{J}\)

3. \(16~\text{J}\)

4. \(20~\text{J}\)

1. \(24~\text{J}\)

2. \(36~\text{J}\)

3. \(16~\text{J}\)

4. \(20~\text{J}\)

Subtopic: Energy of SHM |

66%

From NCERT

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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 |

From NCERT

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A particle executing simple harmonic motion has a kinetic energy of \(K_0 \cos^2(\omega t)\). The values of the maximum potential energy and the total energy are, respectively:

1. \(0~\text{and}~2K_0\)

2. \(\frac{K_0}{2}~\text{and}~K_0\)

3. \(K_0~\text{and}~2K_0\)

4. \(K_0~\text{and}~K_0\)

1. \(0~\text{and}~2K_0\)

2. \(\frac{K_0}{2}~\text{and}~K_0\)

3. \(K_0~\text{and}~2K_0\)

4. \(K_0~\text{and}~K_0\)

Subtopic: Energy of SHM |

62%

From NCERT

AIPMT - 2007

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A point performs simple harmonic oscillation of period \(\mathrm{T}\) and the equation of motion is given by; \(x=a \sin (\omega t+\pi / 6)\). After the elapse of what fraction of the time period, the velocity of the point will be equal to half of its maximum velocity?

1. \( \frac{T}{8} \)

2. \( \frac{T}{6} \)

3. \(\frac{T}{3} \)

4. \( \frac{T}{12}\)

Subtopic: Linear SHM |

70%

From NCERT

AIPMT - 2008

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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. \(2\pi \sqrt{\frac{q}{p}}\)

2. \(2\pi \sqrt{\frac{p}{q}}\)

3. \(2\pi \sqrt{\frac{q}{p+q}}\)

4. \(2\pi \sqrt{\frac{p}{p+q}}\)

1. \(2\pi \sqrt{\frac{q}{p}}\)

2. \(2\pi \sqrt{\frac{p}{q}}\)

3. \(2\pi \sqrt{\frac{q}{p+q}}\)

4. \(2\pi \sqrt{\frac{p}{p+q}}\)

Subtopic: Energy of SHM |

73%

From NCERT

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The period of oscillation of a mass \(M\) suspended from a spring of negligible mass is \(T\). If along with it, another mass \(M\) is also suspended, the period of oscillation will now be:

1. \(T\)

2. \(\frac{T}{\sqrt{2}}\)

3. \(2T\)

4. \(\sqrt{2}T\)

1. \(T\)

2. \(\frac{T}{\sqrt{2}}\)

3. \(2T\)

4. \(\sqrt{2}T\)

Subtopic: Spring mass system |

79%

From NCERT

AIPMT - 2010

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