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Set 13 of 13 · Questions 361-372 of 372

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JEE Main Physics · Simple Harmonic Motion · Set 13 (Q361-372)

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  1. 361.
    A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position . Consider two cases: (i) when the block is at ; and (ii) when the block is at x = + A. In both the cases, a particle with mass m (< M) is softly placed on the block after which they stick to each other. Which of the following statement(s) is(are) true about the motion after the mass m is placed on the mass M?
    1. (1)The amplitude of oscillation in the first case changes by a factor of , whereas in the second case it remains unchanged
    2. (2)The final time period of oscillation in both the cases is same
    3. (3)The total energy decreases in both the cases
    4. (4)The instantaneous speed at of the combined masses decreases in both the cases
  2. 362.
    The S.H.M. of a particle is given by the equation . The amplitude is
    1. (1)7
    2. (2)1
    3. (3)5
    4. (4)12
  3. 363.
    The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.

    The potential energy versus time plot of the particle is correctly shown in figure:
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  4. 364.
    A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in second is:
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  5. 365.
    The amplitude of a particle due to superposition of following S.H.Ms. Along the same line is
    = 2 sin 50πt ; = 10 sin (50 πt + 37º)
    = - 4 sin 50πt ; = - 12 cos 50πt
    1. (1)4
    2. (2)4
    3. (3)6
    4. (4)none of these
  6. 366.
    When two displacement represented by = a sin (ꞷt) and = b cos (ꞷt) are superimposed the motion is
    1. (1)simple harmonic with amplitude
    2. (2)simple harmonic with amplitude
    3. (3)simple harmonic with amplitude
    4. (4)not a simple harmonic
  7. 367.
    A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ꞷ. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time:
    1. (1)at the highest position of the platform
    2. (2)at the mean position of the platform
    3. (3)for an amplitude of
    4. (4)for an amplitude of
  8. 368.
    A simple pendulum is set into vibrations. The bob of the pendulum comes to rest after some time due to:
    1. (1)Air friction
    2. (2)Moment of inertia
    3. (3)Weight of the bob
    4. (4)Combination of all the above
  9. 369.
    The resultant of two rectangular simple harmonic motions of the same frequency and unequal amplitudes but differing in phase by is
    1. (1)simple harmonic
    2. (2)circular
    3. (3)elliptical
    4. (4)parabolic
  10. 370.
    A block is in simple harmonic motion (S.H.M) on the end of the spring with position given by (5) . If the total mechanical energy used is to achieve maximum displacement, then the potential energy at time is
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  11. 371.
    A block of mass is connected to an elastic spring of spring constant oscillates vertically. The block-spring system is in viscous surrounding medium with a damping constant . The time in which the amplitude of oscillations drop to half of its initial value. [take ]
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  12. 372.
    A simple pendulum oscillates in air with time period T and amplitude A. As the time passes
    1. (1)T and A both decrease
    2. (2)T increases and A is constant
    3. (3)T increases and A decreases
    4. (4)T decreases and A is constant