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NEET-XI-Physics

14: Oscillations

 page 2

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  • #4-3
    (c) 3 cos -2 cos (``\pi``/4-2 wt)
    Ans :
     
  • #4-4
    (d) cos wt + cos 3 wt + cos 5 wt

    Ans :
  • #4-5
    (e) ``e^{-w^2t^2}``
    Ans : (e) e-w2t2 . It is an exponential function which never repeats itself. Therefore it represents non-periodic motion.

  • #4-6
    (f) 1 + wt + w2t2.
    Ans : (f) 1 + wt + w2t2 also represents non periodic motion.
  • Qstn #5
    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 and give the signs of velocity, acceleration and force on the particle when it is
    Ans : In the fig. (given below), the points A and B, 10 cm apart, are the extreme positions of the particle in SHM, and the point O is the mean position. The direction from A to B is positive, as indicated.


  • #5-a
    at the end A,
    Ans : At the end A, i.e., extreme position, velocity is zero, acceleration and force are directed towards O and are positive.


  • #5-b
    at the end B,
    Ans : At the end B, i.e., second extreme position, velocity is zero whereas the acceleration and force are directed towards the point O and are negative.

  • #5-c
    at the mid-point of AB going towards A,
    Ans : At the mid point O, while going towards A, velocity is negative and maximum. The acceleration and force both are zero.

  • #5-d
    at 2 cm away from B going towards A,
    Ans : At 2 cm away from B, that is, at C and going towards A: v is negative; acceleration and F, being directed towards O, are also negative.

  • #5-e
    at 3 cm away from A going towards B, and
    Ans : At 3 cm away from A, that is, at D and going towards B: v is positive; acceleration and F, being directed towards O, are also positive.

  • #5-f
    at 4 cm away from B going towards A.
    Ans : At a distance of 4 cm away from A and going towards A, velocity is directed along BA, therefore, it is positive. Since acceleration and force are directed towards OB, both of them are positive.

  • Qstn #6
    Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?

    -(a) a = 0.7x (b) a = - 200 x2

    (c) a = - 10x (d) a = 100 x3
    Ans : Only (c) i.e., a = - 10x represents SHM. This is because acceleration is proportional and opposite to displacement (x).
  • Qstn #7
    The motion of a particle executing simple harmonic motion is described by the displacement function.
    x(t) = A cos (wt +Ф ).
    If the initial (t = 0) position of the particle is 1 cm and its initial velocity is w cm/s, what are its amplitude and initial phase angle? The angular frequency of the particle is ``\pi`` s-1. If instead of the cosine function, we choose the sine function to describe the SHM: x = B sin (wt + α), what are the amplitude and initial phase of the particle with the above initial conditions?
    Ans :
  • Qstn #8
    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?
    Ans :


  • Qstn #9
    A spring having with a spring constant 1200 Nm-1 is mounted on a horizontal table as shown in Fig. 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.Determine (i) the frequency of oscillations, (ii) maximum acceleration of the mass, and (iii) the maximum speed of the mass.


    Ans :
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