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NEET-XI-Physics

14: Oscillations

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  • Qstn #1
    Which of the following examples represent periodic motion ?
  • #1-a
    A swimmer completing one (return) trip from one bank of a river to the other and back.
    Ans : It is not a periodic motion. Though the motion of a swimmer is to and fro but will not have a definite period.
  • #1-b
    A freely suspended bar magnet displaced from its’N-S direction and released.
    Ans : Since a freely suspended magnet if once displaced from N-S direction and released, it oscillates about this position, it is a periodic motion
  • #1-c
    A hydrogen molecule rotating about its centre of mass.
    Ans : The rotating motion of a hydrogen molecule about its centre of mass is periodic.
  • #1-d
    An arrow released from a bow.
    Ans : Motion of an arrow released from a bow is non-periodic.
  • Qstn #2
    Which of the following examples represent (nearly) simple harmonic motion and which represent

    periodic but not simple harmonic motion ?
  • #2-a
    the rotations of earth about its axis.
    Ans : Since the rotation of earth is not to and fro motion about a fixed point, thus it is periodic but not S.H.M.
  • #2-b
    motion of an oscillating mercury column in a U-tube.
    Ans : It is S.H.M.
  • #2-c
    motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower most point.
    Ans : It is S.H.M.
  • #2-d
    general vibrations of a polyatomic molecule about its equilibrium position.
    Ans : General vibrations of a polyatomic molecule about its equilibrium position is periodic but non SHM. In fact, it is a result of superposition of SHMs executed by individual vibrations of atoms of the molecule.


  • Qstn #3
    Fig. depicts four x-t plots for linear motion of a particle. Which of ike plots represent periodic motion? What is the period of motion (in case of periodic motion)?




    Ans : Figure (b) and (d) represent periodic motions and the time period of each of these is 2 seconds, (a) and (c) are non-periodic motions.
  • #4-0
    Which of the following function of time represent |a) simple harmonic,(b)periodic but not simple harmonic, and non-periodic motion? Give period for each case of periodic motion (to is any positive constant).

     
    Ans : The function will represent a periodic motion, if it is identically repeated after a fixed interval of time and will represent S.H.M if it can be written uniquely in the form of a cos



     
  • #4-1
    (a) sin wt - cos wt
    Ans : ``\sin \omega t - \cos \omega t``

    =``\sin\omega t - \sin(\pi/2 -\omega t)``     ( as ``cos (\pi/2-\theta) = \sin \theta``)

    (Again (`` \sin A - \sin B = 2\sin \frac{A-B}{2} \cos\frac{A+B}{2}``)
    =``2 \cos \pi/4  \sin(\omega t - \pi/4)``

    = ``\sqrt{2}  \sin(\omega t - \pi/4)``
    ( shm equation ``x(t) = a\sin(\omega t + \alpha)``
    comparing with shm,
    A= ``\sqrt2``  and  Time period T = ``2\pi/\omega`` and phase angle = ``\pi/4``  or ``( 2\pi-\pi/4) = 7\pi/4``.



  • #4-2
    (b) sin3 wt
    Ans :
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