The displacement of a particle in a periodic motion is given by&n

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 Multiple Choice QuestionsMultiple Choice Questions

251.

The displacement of a particle is SHM varies according to the relation x = 4 (cos πt + sin πt). The amplitude of the particle is 

  • − 4

  • 4

  • 42

  • 8


252.

What is the phase difference between two simple harmonic motions represented by x1 = A sin ωt + π6 and x2 = A cos (ωt) ?

  • π6

  • π3

  • π2

  • 2π3


253.

When a spring is stretched by 10 cm, the potential energy stored is E. When the spring is stretched by 10 cm more, the potential energy stored in the spring becomes

  • 2 E

  • 4 E

  • 6 E

  • 10 E


254.

When a particle executing SHM oscillates with a frequency v, then the kinetic energy of the particle

  • changes periodically with a frequency of v

  • changes periodically with a frequency of 2v

  • changes periodically with a frequency of v/2

  • remains constant


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255.

The displacement of a particle in a periodic motion is given by y = 4 cos2 t2 sin 1000 t. This displacement may be considered as the result of superposition of n independent harmonic oscillations. Here n is

  • 1

  • 2

  • 3

  • 4


C.

3

Given,     Y = 4 cos2 t2 . sin 1000 t                  = 2 × 2 cos2 t2 . sin 1000 t   2 cos2 t2 = 1 + cos t                  = 2 1 + cos t sin 1000 t                  = 2 sin 1000 t + 2 cos t . sin  1000 t                  = 2 sin 1000 t + 2 sin 1000 t . cos t                  = 2 sin 1000 t + sin 1000 t + t  + sin (1000 t - t)                                   2 sin A . cos B = sin (A + B) + sin (A - B)                  = 2 sin (1000 t) + sin (1001 t) + sin (999 t)So,          n = 3      


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256.

A simple pendulum of length L swings in a vertical plane. The tension of the string when it makes an angle θ with the vertical and the bob of mass in moves with a speed v is (g is the gravitational acceleration)

  • mv2/L

  • mg cos θ + mv2 / L

  • mg cos θ − mv2 / L

  • mg cos θ


257.

The displacement x of a particle varies with time t as, x = ae-αt +b e βt where a, b α and β are positive constants. The velocity of the particle will

  • go on decreasing with time

  • be independent of α and β

  • drop to zero when α = β

  • go on increasing with time


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